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We show that the effective potentials for the Polyakov loops in finite temperature SU$(N)$ gauge theories obey a certain scaling relation with respect to temperature in the large-$N$ limit. This scaling relation strongly constrains the possible terms in the Polyakov loop effective potentials. Moreover, by using the effective potentials in the presence of imaginary chemical potentials or imaginary angular velocities in several models, we find that phase transitions to $Z_m$-type deconfinement phases ($Z_m$ phase) occur, where the eigenvalues of the Polyakov loop are distributed $Z_m$ symmetrically. Physical quantities in the $Z_m$ phase obey the scaling properties of the effective potential. The models include Yang-Mills (YM) theories, the bosonic BFSS matrix model and ${\mathcal N}=4$ supersymmetric YM theory on $S^3$. Thus, the phase diagrams of large-$N$ gauge theories with imaginary chemical potentials are very rich and the stable $Z_m$ phase would be ubiquitous. Monte-Carlo calculations also support this. As a related topic, we discuss the phase diagrams of large-$N$ YM theories with real angular velocities in finite volume spaces., Comment: 30+16 pages, 15 figures, related movies are on https://www2.yukawa.kyoto-u.ac.jp/~takehiro.azuma/multi_cut/index.html v2: minor corrections v3: version accepted for publication in PTEP

Highly efficient anti-Stokes (AS) photoluminescence (PL) is observed from halide perovskite quantum dots (QDs) due to their strong electron-phonon interactions. The AS PL is particularly intriguing as it suggests the potential for semiconductor optical cooling if the external quantum efficiency approaches 100%. However, the PL quantum efficiency in QDs is primarily dominated by multiparticle nonradiative Auger recombination processes under intense photoexcitation, which impose limits on the optical cooling gain. Here, we investigate the Auger recombination of dot-in-crystal perovskites. We quantitatively estimate the maximum optical cooling gain and the corresponding excitation intensity. We further conducted optical cooling experiments and demonstrate a maximum photo-cooling of approximately 9 K from room temperature. Additionally, we confirmed that increasing the excitation intensity leads to a transition from photo-cooling to photo-heating. These observations are consistent with our time-resolved measurements, offering insights into the potential and limitations of optical cooling in semiconductor QDs.

We consider a low energy effective theory of $p$-branes in a $D$-dimensional spacetime, and impose two conditions: 1) the theory is scale invariant, and 2) the electric-magnetic dual $(D-p-4)$-branes exist and they obey the same type of interactions to the $p$-branes. (We also assume other natural conditions such as Lorentz invariance but not string theory, supersymmetry, supergravity and so on.) We then ask what $p$ and $D$ are consistent with these conditions. Using simple dimensional analysis, we find that only two solutions are possible: $(p,D)=(2,11)$ and $(p,D)=(2n-1,4n+2)$, ($n=1,2,3,\cdots$). The first solution corresponds to M-theory, and the second solutions at $n=1$ and $n=2$ correspond to self-dual strings in little string theory and D3-branes in type IIB superstring theory, respectively, while the second solutions for $n \ge 3$ are unknown but would be higher spin theories. Thus, quantum gravity (massless spin two theory) satisfying our two conditions would only be superstring theories, and the conditions would be strong enough to characterize superstring theories in quantum gravity., Comment: 8+3 pages, 2 figures, v2: minor changes, v3: title changes, version accepted for publication in PTEP, v4: a typo has been corrected

Rotating systems in thermal equilibrium are ubiquitous in our world. In the context of high energy physics, rotations would affect the phase structure of QCD. However, the standard Monte-Carlo methods in rotating systems are problematic because the chemical potentials for the angular momenta (angular velocities) cause sign problems even for bosonic variables. In this article, we demonstrate that the complex Langevin method (CLM) may overcome this issue. We apply the CLM to the Yang-Mills (YM) type one-dimensional matrix model (matrix quantum mechanics) that is a large-$N$ reduction (or dimensional reduction) of the $(D+1)$-dimensional U$(N)$ pure YM theory (bosonic BFSS model). This model shows a large-$N$ phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory, and our CLM predicts that the transition temperature decreases as the angular momentum chemical potential increases. In order to verify our results, we compute several quantities via the minimum sensitivity method and find good quantitative agreements. Hence, the CLM properly works in this rotating system. We also argue that our results are qualitatively consistent with a holography and the recent studies of the imaginary angular velocity in QCD. As a byproduct, we develop an analytic approximation to treat the so-called ``small black hole" phase in the matrix model., Comment: 31 + 13 pages,16 figures. v2: minor corrections. v3: section 5 revised. v4: minor corrections, published version

The range of motion of a particle with certain energy $E$ confined in a potential is determined from the energy conservation law in classical mechanics. The counterpart of this question in quantum mechanics can be regarded as what the possible range of the expectation values of the position operator $ \langle x \rangle$ of a particle, which satisfies $E= \langle H \rangle$. This range depends on the state of the particle, but the universal upper and lower bounds, which is independent of the state, must exist. In this study, we show that these bounds can be derived by using the bootstrap method. We also point out that the bootstrap method can be regarded as a generalization of the uncertainty relations, and it means that the bounds are determined by the uncertainty relations in a broad sense. Furthermore, the bounds on possible expectation values of various quantities other than position can be determined in the same way. However, in the case of multiple identical particles (bosons and fermions), we find some difficulty in the bootstrap method. Because of this issue, the predictive power of the bootstrap method in multi-particle systems is limited in the derivation of observables including energy eigenstates. In addition, we argue an application of the bootstrap method to thermal equilibrium states. We find serious issues that temperature and entropy cannot be handled. Although we have these issues, we can derive some quantities in micro-canonical ensembles of integrable systems governed by generalized Gibbs ensembles., Comment: 35 pages, 12 figures, v2: numerical analysis in sec.3.1.2 was revised, v3: title changed, references added, parts of sec 4.3 shifted to appendix B, matches published version

Recently, an application of the numerical bootstrap method to quantum mechanics was proposed, and it successfully reproduces the eigenstates of various systems. However, it is unclear why this method works. In order to understand this question, we study the bootstrap method in harmonic oscillators. We find that the problem reduces to the Dirac's ladder operator problem and is exactly solvable analytically. Our result suggests that the bootstrap method may be regarded as a numerical version of the Dirac's approach and it may explain why it works in various systems., Comment: 12 pages, no figures, v2 bootstrap analysis in an anharmonic oscillator by using ladder operators added and an appendix on constructing bootstrap matrix in a general polynomial potential added

Recently, novel numerical computation on quantum mechanics by using a bootstrap method was proposed by Han, Hartnoll, and Kruthoff. We consider whether this method works in systems with a $\theta$-term, where the standard Monte-Carlo computation may fail due to the sign problem. As a starting point, we study quantum mechanics of a charged particle on a circle in which a constant gauge potential is a counterpart of a $\theta$-term. We find that it is hard to determine physical quantities as functions of $\theta$ such as $E(\theta)$, except at $\theta=0$ and $\pi$. On the other hand, the correlations among observables for energy eigenstates are correctly reproduced for any $\theta$. Our results suggest that the bootstrap method may work not perfectly but sufficiently well, even if a $\theta$-term exists in the system., Comment: 16 pages, 5 figures.v3: matches published version in PRD, appendix on the details of the numerical bootstrap was added

The commutator $[x(t),p]$ in an inverted harmonic oscillator (IHO) in one-dimensional quantum mechanics exhibits remarkable properties. It reduces to a c-number and does not show any quantum fluctuations for arbitrary states. Related to this nature, the quantum Lyapunov exponent computed through the out-of-time-order correlator (OTOC) $\langle [x(t),p]^2 \rangle $ precisely agrees with the classical one. Hence, the OTOC may be regarded as an ideal indicator of the butterfly effect in the IHO. Since IHOs are ubiquitous in physics, these properties of the commutator $[x(t),p]$ and the OTOCs might be seen in various situations, too. In order to clarify this point, as a first step, we investigate OTOCs in one-dimensional quantum mechanics with polynomial potentials, which exhibit butterfly effects around the peak of the potential in classical mechanics. We find two situations in which the OTOCs show exponential growth reproducing the classical Lyapunov exponent of the peak. The first one, which is obvious, is using a suitably localized wave packet near the peak, and the second one is taking a limit akin to the large-$N$ limit in the noncritical string theories., Comment: 15 pages, 5 figures. Appendix moved to the main text,the version published in PRD

We propose that Hawking radiation-like phenomena may be observed in systems that show butterfly effects. Suppose that a classical dynamical system has a Lyapunov exponent $\lambda_L$, and is deterministic and non-thermal ($T=0$). We argue that, if we quantize this system, the quantum fluctuations may imitate thermal fluctuations with temperature $T \sim \hbar \lambda_L/2 \pi $ in a semi-classical regime, and it may cause analogous Hawking radiation. We also discuss that our proposal may provide an intuitive explanation of the existence of the bound of chaos proposed by Maldacena, Shenker and Stanford., Comment: 9 pages, 4 figures, Proceedings of 4th International Conference on Holography, String Theory and Discrete Approach in Hanoi (3-8 August 2020)

We investigate critical phenomena of the Yang-Mills (YM) type one-dimensional matrix model that is a large-$N$ reduction (or dimensional reduction) of the $D+1$ dimensional $U(N)$ pure YM theory (bosonic BFSS model). This model shows a large-$N$ phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory. We study the matrix model at a three-loop calculation via the "principle of minimum sensitivity" and find that there is a critical dimension $D=35.5$: At $D \le 35$, the transition is of first order, while it is of second order at $D\ge 36$. Furthermore, we evaluate several observables in our method, and they nicely reproduce the existing Monte Carlo results. Through the gauge/gravity correspondence, the transition is expected to be related to a Gregory-Laflamme transition in gravity, and we argue that the existence of the critical dimension is qualitatively consistent with it. Besides, in the first order transition case, a stable phase having negative specific heat appears in the microcanonical ensemble, which is similar to Schwarzschild black holes. We study some properties of this phase., Comment: 12 pages, 6 figures, v2: minor corrections, v3: minor corrections and reference added, v4: published version, Discussions on negative specific heat are added

A new method to study nuclear physics via holographic QCD is proposed. Multiple baryons in the Sakai-Sugimoto background are described by a matrix model which is a low energy effective theory of D-branes of the baryon vertices. We study the quantum mechanics of the matrix model and calculate the eigenstates of the Hamiltonian. The obtained states are found to coincide with known nuclear and baryonic states, and have appropriate statistics and charges. Calculated spectra of the baryon/nucleus for small baryon numbers show good agreement with experimental data. For hyperons, the Gell-Mann--Okubo formula is approximately derived. Baryon resonances up to spin $5/2$ and isospin $5/2$ and dibaryon spectra are obtained and compared with experimental data. The model partially explains even the magic numbers of light nuclei, $N=2,8$ and $20$., Comment: 65 pages; v2: 69 pages, discussions on the magic number are clarified; v3: 75 pages, published version

Recently the bound on the Lyapunov exponent $\lambda_L \le 2\pi T/ \hbar$ in thermal quantum systems was conjectured by Maldacena, Shenker, and Stanford. If we naively apply this bound to a system with a fixed Lyapunov exponent $\lambda_L$, it might predict the existence of the lower bound on temperature $T \ge \hbar \lambda_L/ 2\pi $. Particularly, it might mean that chaotic systems cannot be zero temperature quantum mechanically. Even classical dynamical systems, which are deterministic, might exhibit thermal behaviors once we turn on quantum corrections. We elaborate this possibility by investigating semi-classical particle motions near the hyperbolic fixed point and show that indeed quantum corrections may induce energy emission which obeys a Boltzmann distribution. We also argue that this emission is related to acoustic Hawking radiation in quantum fluid. Besides, we discuss when the bound is saturated and show that a particle motion in an inverse harmonic potential and $c=1$ matrix model may saturate the bound although they are integrable., Comment: 5 pages, 3 figures, published version

By exploring a phase space hydrodynamics description of one-dimensional free Fermi gas, we discuss how systems settle down to steady states described by the generalized Gibbs ensembles through quantum quenches. We investigate time evolutions of the Fermions which are trapped in external potentials or a circle for a variety of initial conditions and quench protocols. We analytically compute local observables such as particle density and show that they always exhibit power law relaxation at late times. We find a simple rule which determines the power law exponent. Our findings are, in principle, observable in experiments in an one dimensional free Fermi gas or Tonk's gas (Bose gas with infinite repulsion)., Comment: 29 pages, 9 figures, v2: published version

In our previous work arXiv:1704.08675, we pointed out that various multi-cut solutions exist in the Chern-Simons (CS) matrix models at large-$N$ due to a curious structure of the saddle point equations. In the ABJM matrix model, these multi-cut solutions might be regarded as the condensations of the D2-brane instantons. However many of these multi-cut solutions including the ones corresponding to the condensations of the D2-brane instantons were obtained numerically only. In the current work, we propose an ansatz for the multi-cut solutions which may allow us to derive the analytic expressions for all these solutions. As a demonstration, we derive several novel analytic solutions in the pure CS matrix model and the ABJM matrix model. We also develop the argument for the connection to the instantons., Comment: 43 pages, 16 figures, v2: published version, minor changes

Classical particle motions in an inverse harmonic potential show the exponential sensitivity to initial conditions, where the Lyapunov exponent $\lambda_L$ is uniquely fixed by the shape of the potential. Hence, if we naively apply the bound on the Lyapunov exponent $\lambda_L \le 2\pi T/ \hbar$ to this system, it predicts the existence of the bound on temperature (the lowest temperature) $T \ge \hbar \lambda_L/ 2\pi$ and the system cannot be taken to be zero temperature when $\hbar \neq 0$. This seems a puzzle because particle motions in an inverse harmonic potential should be realized without introducing any temperature but this inequality does not allow it. In this article, we study this problem in $N$ non-relativistic free fermions in an inverse harmonic potential ($c=1$ matrix model). We find that thermal radiation is {\em induced} when we consider the system in a semi-classical regime even though the system is not thermal at the classical level. This is analogous to the thermal radiation of black holes, which are classically non-thermal but behave as thermal baths quantum mechanically. We also show that the temperature of the radiation in our model saturates the inequality, and thus, the system saturates the bound on the Lyapunov exponent, although the system is free and integrable. Besides, this radiation is related to acoustic Hawking radiation of the fermi fluid., Comment: v3: 18+11 pages, 6 figures introduction was modified, accepted version

We elaborate the Chern-Simons (CS) matrix models at large $N$. The saddle point equations of these matrix models have a curious structure which cannot be seen in the ordinary one matrix models. Thanks to this structure, an infinite number of multi-cut solutions exist in the CS matrix models. Particularly we exactly derive the two-cut solutions at finite 't\,Hooft coupling in the pure CS matrix model. In the ABJM matrix model, we argue that some of multi-cut solutions might be interpreted as a condensation of the D2-brane instantons., Comment: 25 pages, 9 figures; v2: published version, minor changes

This study presents the development of large-area (18 $\times $ 18 $\times $ 2 cm$^3$), high refractive index ($n \sim $1.05) hydrophobic silica aerogel tiles for use as Cherenkov radiators. These transparent aerogel tiles will be installed in a Cherenkov detector for the next-generation accelerator-based particle physics experiment Belle II, to be performed at the High Energy Accelerator Research Organization (KEK) in Japan. Cracking has been eliminated from the prototype aerogel tiles by improving the supercritical carbon dioxide (scCO$_2$) extraction procedure when drying the wet gel tiles. Finally, a method of mass-producing aerogel tiles for the actual detector was established. It was confirmed that the experimentally manufactured aerogel tiles meet the required optical and hydrophobic characteristics and have a uniform tile density., Comment: Published in Journal of Supercritical Fluids, 14 pages, 14 figures, 3 tables

We provide new formulae for the degenerations of the bilateral basic hypergeometric function ${}_1\psi_1 ( a; b; q, z )$ with using the $q$-Borel-Laplace transformation. These are thought of as the first step to construct connection formulae of $q$-difference equation for ${}_1\psi_1 ( a; b; q, z )$. Moreover, we show that our formulae have the $q \to 1 - 0$ limit., Comment: 13 pages

We give summation formulae for the bilateral basic hypergeometric series ${}_1\psi_1( a; b; q, z )$ through Ramanujan's summation formula, which are generalizations of nontrivial identities found in the physics of three-dimensional Abelian mirror symmetry on $\mathbf{R}P^2 \times S^1$. We also show the $q \to 1 - 0$ limit of our summation formulae., Comment: 17 pages

The supercoonformal index on $\mathbb{RP}^{2} \times \mathbb{S}^{1}$ can be derived exactly by the localization technique and applied to the direct proof of Abelian mirror symmetry. We find two sets of parity conditions compatible with the unorientable property of $\mathbb{RP}^{2}$ and then rigorously show two kinds of Abelian mirror symmetry via the index on $\mathbb{RP}^{2} \times \mathbb{S}^{1}$., Comment: 6 pages, contribution to proceedings of IX International Symposium on Quantum Theory and Symmetries

In the present paper, we introduce a multibasic extension of the Ehrhart theory. We give a multibasic extension of Ehrhart polynomials and Ehrhart series. We also show that an analogue of Ehrhart reciprocity holds for multibasic Ehrhart polynomials.

Till date, the only consistent description of the deconfinement phase of the Sakai-Sugimoto model appears to be provided by the analysis of [1] (arXiv:1107.4048). The current version of the analysis, however, has a subtlety regarding the monodromy of quarks around the Euclidean time circle. In this note, we revisit and resolve this issue by considering the effect of an imaginary baryon chemical potential on quark monodromies. With this ingredient, the proposal of [1] for investigating finite temperature QCD using holography is firmly established. Additionally, our technique allows a holographic computation of the free energy as a function of the imaginary chemical potential in the deconfinement phase; we show that our result agrees with the corresponding formula obtained from perturbative QCD, namely the Roberge-Weiss potential., Comment: 18 pages, 2 figures

If an Einstein-Maxwell-Dilaton system admits the extreme brane solution in which no force works between the parallel branes, the collective motion of nearly parallel branes exhibits the thermodynamical properties which are coincident with those of the corresponding black branes at low energy regime (up to unfixed numerical factors). Hence it may provide the microscopic description of the black branes ($p$-soup proposal). This fact motivates us to test this proposal in the intersecting black branes which have multiple brane charges and/or momentum along the brane direction. We consider the case that the multiple branes satisfy the intersection rule and feel no force when they are static, and find the agreement to the black hole thermodynamics., Comment: 1+17 pages

We consider a new 3d superconformal index defined as the path integral over $\mathbb{RP}^2 \times \mathbb{S}^1$, and get the generic formula for this index with arbitrary number of U$(1)$ gauge symmetries via the localization technique. We find two consistent parity conditions for the vector multiplet, and name them $\mathcal{P}$ and $\mathcal{CP}$. We find an interesting phenomenon that two matter multiplets coupled to the $\mathcal{CP}$-type vector multiplet merge together. By using this effect, we investigate the simplest version of 3d mirror symmetry on $\mathbb{RP}^2 \times \mathbb{S}^1$ and observe four types of coincidence between the SQED and the XYZ model. We find that merging two matters plays an important role for the agreement., Comment: 28 pages, formulas modified and comments added

We investigate instantons in finite temperature QCD via Witten's holographic QCD. To study the deconfinement phase, we use the setup proposed in [1] (arXiv:1107.4048). We find that the sizes of the instantons are stabilized at certain values both in the confinement and deconfinement phases. This agrees with the numerical result in the lattice gauge theory. Besides we find that the gravity duals of the large and small instantons in the deconfinement phase have different topologies. We also argue that the fluctuation of the topological charges is large in confinement phase while it is exponentially suppressed in deconfinement phase, and a continuous transition occurs at the Gross-Witten-Wadia (GWW) point. It would be difficult to observe the counterpart of this transition in lattice QCD, since the GWW point in QCD may stay at an unstable branch., Comment: 25 pages, 4 figures; v2: references added, minor corrections

Maximally supersymmetric (p+1)-dimensional Yang-Mills theory at large N and finite temperature, with possibly compact spatial directions, has a rich phase structure. Strongly coupled phases may have holographic descriptions as black branes in various string duality frames, or there may be no gravity dual. In this paper we provide tools in the gauge theory which give a simple and unified picture of the various strongly coupled phases, and transitions between them. Building on our previous work we consider the effective theory describing the moduli of the gauge theory, which can be computed precisely when it is weakly coupled far out on the Coulomb branch. Whilst for perturbation theory naive extrapolation from weak coupling to strong gives little information, for this moduli theory naive extrapolation from its weakly to its strongly coupled regime appears to encode a surprising amount of information about the various strongly coupled phases. We argue it encodes not only the parametric form of thermodynamic quantities for these strongly coupled phases, but also certain transcendental factors with a geometric origin, and allows one to deduce transitions between the phases. We emphasise it also gives predictions for the behaviour of a large class of local operators in these phases., Comment: 64 pages, 3 figures

In our previous study [1] (1311.6540), we figured out that the thermodynamics of the near extremal black $p$-branes can be explained as the collective motions of gravitationally interacting elementary $p$-branes (the $p$-soup proposal). We test this proposal in the near-extremal D1-D5 and D1-D5-P black holes and show that their thermodynamics also can be explained in a similar fashion, i.e. via the collective motions of the interacting elementary D1-branes and D5-branes (and waves). It may imply that the microscopic origins of these intersecting black branes and the black $p$-brane are explained in the unified picture. We also argue the relation between the $p$-soup proposal and the conformal field theory calculations of the D1-D5(-P) black holes in superstring theory., Comment: 1+11 pages, no figures; v2: minor corrections

We study gauge and gravity backreaction in a holographic model of quantum quench across a superfluid critical transition. The model involves a complex scalar field coupled to a gauge and gravity field in the bulk. In earlier work (arXiv:1211.1776) the scalar field had a strong self-coupling, in which case the backreaction on both the metric and the gauge field can be ignored. In this approximation, it was shown that when a time dependent source for the order parameter drives the system across the critical point at a rate slow compared to the initial gap, the dynamics in the critical region is dominated by a zero mode of the bulk scalar, leading to a Kibble-Zurek type scaling function. We show that this mechanism for emergence of scaling behavior continues to hold without any self-coupling in the presence of backreaction of gauge field and gravity. Even though there are no zero modes for the metric and the gauge field, the scalar dynamics induces adiabaticity breakdown leading to scaling. This yields scaling behavior for the time dependence of the charge density and energy momentum tensor., Comment: 25 pages; v2 minor corrections; v3 minor corrections, to appear in JHEP

We study $\mathcal{N} = 2$ supersymmetric gauge theories on $\mathbb{RP}^2 \times \mathbb{S}^1$ and compute the superconformal index by using the localization technique. We consider not only the round real projective plane $\mathbb{RP}^2$ but also the squashed real projective plane $\mathbb{RP}^2_b$ which turns back to $\mathbb{RP}^2$ by taking a squashing parameter $b$ as $1$. In addition, we found that the result is independent of the squashing parameter $b$. We apply our new superconformal index to the check of the simplest 3d mirror symmetry, i.e. the equivalence between the $\mathcal{N}=2$ SQED and the XYZ model on $\mathbb{RP}^2 \times \mathbb{S}^1$. We prove it by using a mathematical formula called the $q$-binomial theorem. We comment on the $\mathcal{N}=4$ version of mirror symmetry, mirror symmetry via generalized indices, and possibilities of generalizations from mathematical viewpoints., Comment: 47 pages; v2: discussions and references added; v3: discussions added and published in Physical Review D

We show connection formulae of local solutions of the Ramanujan equation between the origin and the infinity. These solutions are given by the Ramanujan function, the $q$-Airy function and the divergent basic hypergeometric series ${}_2\varphi_0(0,0;-;q,x)$. We use two different $q$-Borel-Laplace resummation methods to obtain our connection formulae. We also introduce the $q$-Borel-Laplace transformation of level $r-1$, which are higher order extension of these transformations. These methods are useful to obtain an asymptotic formula of a divergent series ${}_r\varphi_0(0,0,\dots ,0;-;q,x)$., Comment: arXiv admin note: substantial text overlap with arXiv:1203.3404

It is expected that the Gregory-Laflamme (GL) instability in the black string in gravity is related to the Rayleigh-Plateau instability in fluid mechanics. Especially, the orders of the phase transitions associated with these instabilities depend on the number of the transverse space dimensions, and they are of first and second order below and above the critical dimension. Through the gauge-gravity correspondence, the GL instability is conjectured to be thermodynamically related to the Hagedorn instability in large-N gauge theories, and it leads to a prediction that the order of the confinement-deconfinement transition associated with the Hagedorn instability may depend on the transverse dimension. We test this conjecture in the D-dimensional bosonic D0-brane model using numerical simulation and the 1/D expansion, and confirm the expected D dependence., Comment: 5 pages, 11 figures, v3: minor corrections, published by PRL

We give the new connection formula for the divergent bilateral basic hypergeometric series ${}_2\psi_2(a_1,a_2;b_1;q,x)$ by the using of the $q$-Borel-Laplace resummation method and Slater's formula. The connection coefficients are given by elliptic functions.

We show the connection formula for the basic hypergeometric series ${}_3\varphi_1(a_1,a_2,a_3;b_1;q,x)$ between around the origin and infinity by the using of the $q$-Borel-Laplace transformations. We also show the limit $q\to 1-0$ of the new connection formula.

We consider a model of D-dimensional supergravity coupled to elementary p-branes. We use gravitational arguments to deduce the low energy effective theory of N nearly parallel branes. This is a (p+1)-dimensional scalar field theory, where the scalars represent the positions of the branes in their transverse space. We propose that the same theory in a certain temperature regime describes a `soup' of strongly interacting branes, giving a microscopic description of near extremal black p-branes. We use natural approximations to estimate the energy density of this soup as a function of the physical parameters; N, temperature, brane tension and gravitational coupling. We also characterise the horizon radius, measured in the metric natural to the branes, with the thermal vev of the scalars. For both quantities we find agreement with the corresponding supergravity black brane results. Surprisingly, beyond the physical parameters, we are naturally able to reproduce certain irrational factors such as pi's. We comment on how these ideas may explain why black hole thermodynamics arises in gauge theories with holographic duals at finite temperature., Comment: 32 pages, no figures

We discuss thermodynamics of N M2-branes at strong coupling from the ABJM theory by employing the Smilga-Wiseman method, which explains the black Dp-brane thermodynamics from the maximally supersymmetric U(N) Yang-Mills theories through a field theory analysis. As a result we obtain the free energy of the ABJM theory ~N^{3/2}k^{1/2}T^3, which is consistent with the prediction from eleven-dimensional supergravity. We also estimate the free energy of N M5-branes by assuming some natural properties of the 6d superconformal field theory. Remarkably we obtain the free energy ~N^3T^6, which is consistent again with the supergravity prediction. This result might illuminate the low energy field theory description of the multiple M5-branes., Comment: 1+19 pages, v2: new section 5 and references added, v3: minor corrections and a reference added, v4: minor corrections

Quantum quench dynamics is considered in a one dimensional unitary matrix model with a single trace potential. This model is integrable and has been studied in the context of non-critical string theory. We find dynamical phase transitions, and study the role of the quantum critical point. In course of the time evolutions, we find evidence of selective equilibration for a certain class of observables. The equilibrium is governed by the Generalized Gibbs Ensemble (GGE) and differs from the standard Gibbs ensemble. We compute the production of entropy which is O(N) for large N matrices. An important feature of the equilibration is the appearance of an energy cascade, reminiscent of the Richardson cascade in turbulence, where we find flow of energy from initial long wavelength modes to progressively shorter wavelength excitations. We discuss possible implication of the equilibration and of GGE in string theories and higher spin theories. In another related study, we compute time evolutions in a double trace unitary matrix model, which arises as an effective theory of D2 branes in IIA string theory in the confinement phase. We find similar equilibrations and dynamical transitions in this matrix model. The dynamical transitions are related to Gregory-Laflamme transitions in string theory and are potentially connected with the issue of appearance of naked singularities., Comment: 46 pages, 28 figures; v2: minor corrections, references added; related movies are on http://www2.yukawa.kyoto-u.ac.jp/~mtakeshi/MQM/index.html

This paper proposes a new X-ray radiographic technique for measuring density uniformity of silica aerogels used as radiator in proximity-focusing ring-imaging Cherenkov detectors. To obtain high performance in a large-area detector, a key characteristic of radiator is the density (i.e. refractive index) uniformity of an individual aerogel monolith. At a refractive index of n = 1.05, our requirement for the refractive index uniformity in the transverse plane direction of an aerogel tile is |\delta (n - 1)/(n - 1)| < 4% in a focusing dual layer radiator (with different refractive indices) scheme. We applied the radiographic technique to evaluate the density uniformity of our original aerogels from a trial production and that of Panasonic products (SP-50) as a reference, and to confirm they have sufficient density uniformity within \pm 1% along the transverse plane direction. The measurement results show that the proposed technique can quantitatively estimate the density uniformity of aerogels., Comment: To be published in Nucl. Instr. and Meth. A, 8 pages, 6 figures, 1 table

We present optical and X-ray radiographical characterization of silica aerogels with refractive index from 1.05 to 1.07 for a Cherenkov radiator. A novel pin-drying method enables us to produce highly transparent hydrophobic aerogels with high refractive index by shrinking wet-gels. In order to investigate the uniformity in the density (i.e., refractive index) of an individual aerogel monolith, we use the laser Fraunhofer method, an X-ray absorption technique, and Cherenkov imaging by a ring imaging Cherenkov detector in a beam test. We observed an increase in density at the edge of the aerogel tiles, produced by pin-drying., Comment: To be published in IEEE Trans. Nucl. Sci., 7 pages, 9 figures, 1 table

We study a one-dimensional large-N U(N) gauge theory on a circle as a toy model of higher dimensional Yang-Mills theories at finite temperature. To investigate the profile of the thermodynamical potential in this model, we evaluate a stochastic time evolution of several states, and find that an unstable confinement phase at high temperature does not decay to a stable deconfinement phase directly. Before it reaches the deconfinement phase, it develops to several intermediate states. These states are characterised by the expectation values of the Polyakov loop operators, which wind the temporal circle different times. We reveal that these intermediate states are the saddle point solutions of the theory, and similar solutions exist in a wide class of SU(N) and U(N) gauge theories on S^1 including QCD and pure Yang-Mills theories in various dimensions. We also consider a Kaluza-Klein gravity, which is the gravity dual of the one-dimensional gauge theory on a spatial S^1, and show that these solutions may be related to multi black holes localised on the S^1. Then we present a connection between the stochastic time evolution of the gauge theory and the dynamical decay process of a black string though the Gregory-Laflamme instability., Comment: 34 pages, 10 figures, related movies are on http://www2.yukawa.kyoto-u.ac.jp/~azuma/multi_cut/index.html; v2: minor corrections; v3: minor corrections, to appear in JHEP

We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1\psi_0 (a;-;q,\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\to 1-0$ of our asymptotic formula.

We show connection formulae of local solutions of the Ramanujan equation between the origin and the infinity. These solutions are given by the Ramanujan function, the $q$-Airy function and the divergent basic hypergeometric series ${}_2\varphi_0(0,0;-;q,x)$. We use two different $q$-Borel-Laplace transformations to obtain our connection formulae., Comment: arXiv admin note: text overlap with arXiv:1104.0755

We study the gravity dual of four dimensional pure Yang-Mills theory through D4 branes, as proposed by Witten (holographic QCD). In this holographic QCD, it has been widely believed that the confinement phase in the pure Yang-Mills theory corresponds to the AdS D4 soliton in gravity and the deconfinement phase corresponds to the black D4 brane. We inspect this conjecture carefully and show that the correspondence between the black D4 brane and the deconfinement phase is not correct. Instead, by using a slightly different set up, we find an alternative gravity solution called "localized soliton", which would be properly related to the deconfinement phase. In this case, the confinement/deconfinement transition is realized as a Gregory-Laflamme type transition. We find that our proposal naturally explains several known properties of QCD., Comment: 6 pages, 1 figure, based on the proceedings of the Seventh International Conference `Quantum Theory and Symmetries', held in Prague 2011 and XVII European Workshop on String Theory 2011, held in Padua; v2: minor corrections

We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S^3 partition functions. An explicit illustration based on the known analytic solution of the Chern-Simons matrix model is presented., Comment: 42 pages, 12 figures; v2 mostly cosmetic changes, references added; v3 minor changes to match the published version in NPB

We discuss the phase structure of N D4 branes wrapped on a temporal (Euclidean) and a spatial circle, in terms of the near-horizon AdS geometries. This system has been studied previously to understand four dimensional pure SU(N) Yang-Mills theory (YM4) through holography. In the usual treatment of the subject, the phase transition between the AdS soliton and the black D4 brane is interpreted as the strong coupling continuation of the confinement/deconfinement transition in YM4. We show that this interpretation is not valid, since the black D4 brane and the deconfinement phase of YM4 have different realizations of the Z_N centre symmetry and cannot be identified. We propose an alternative gravity dual of the confinement/deconfinement transition in terms of a Gregory-Laflamme transition of the AdS soliton in the IIB frame, where the strong coupling continuation of the deconfinement phase of YM4 is a localized D3 soliton. Our proposal offers a new explanation of several aspects of the thermodynamics of holographic QCD. As an example, we show a new mechanism of chiral symmetry restoration in the Sakai-Sugimoto model. The issues discussed in this paper pertain to gravity duals of non-supersymmetric gauge theories in general., Comment: 45 pages, 10 figures; v2: details of the analysis and new phase diagram in Sakai-Sugimoto model are added. version appeared in JHEP; v3: minor corrections. references are added; v4: minor corrections

We show a connection formula for the $q$-confluent hypergeometric functions ${}_2\varphi_1(a,b;0;q,x)$. Combining our connection formula with Zhang's connection formula for ${}_2\varphi_0(a,b;-;q,x)$, we obtain the connection formula for the $q$-confluent hypergeometric equation in the matrix form. Also we obtain the connection formula of Kummer's confluent hypergeometric functions by taking the limit $q\to 1^{-}$ of our connection formula.

We show a connection formula of the Hahn-Exton $q$-Bessel function around the origin and the infinity. We introduce the $q$-Borel transformation and the $q$-Laplace transformation following C. Zhang to obtain the connection formula. We consider the limit $p\to 1^-$ of the connection formula.

We show a connection formula between two different $q$-Airy functions. One is called the Ramanujan function which appears in Ramanujan's "Lost notebook". Another one is called the $q$-Airy function that obtained in the study of the second $q$-Painlev\'e equation. We use the $q$-Borel transformation and the $q$-Laplace transformation following C. Zhang to obtain the connection formula.

In generic holographic QCD, we find that baryons are bound to form a nucleus, and that its radius obeys the empirically-known mass number (A) dependence r A^{1/3} for large A. Our result is robust, since we use only a generic property of D-brane actions in string theory. We also show that nucleons are bound completely in a finite volume. Furthermore, employing a concrete holographic model (derived by Hashimoto, Iizuka, and Yi, describing a multi-baryon system in the Sakai-Sugimoto model), the nuclear radius is evaluated as O(1) x A^{1/3} [fm], which is consistent with experiments., Comment: 4 pages; Ver.2: terminology on nuclear density saturation modified, a reference added

We consider two-dimensional large N gauge theory with D adjoint scalars on a torus, which is obtained from a D+2 dimensional pure Yang-Mills theory on T^{D+2} with D small radii. The two dimensional model has various phases characterized by the holonomy of the gauge field around non-contractible cycles of the 2-torus. We determine the phase boundaries and derive the order of the phase transitions using a method, developed in an earlier work (arxiv:0910.4526), which is nonperturbative in the 'tHooft coupling and uses a 1/D expansion. We embed our phase diagram in the more extensive phase structure of the D+2 dimensional Yang-Mills theory and match with the picture of a cascade of phase transitions found earlier in lattice calculations (arxiv:0710.0098). We also propose a dual gravity system based on a Scherk-Schwarz compactification of a D2 brane wrapped on a 3-torus and find a phase structure which is similar to the phase diagram found in the gauge theory calculation., Comment: 28 pages (+ 17 pages of appendix + 6 pages of ref.); 8 figures; (v2) LaTeX Showkeys command deleted; (v3) refs and minor clarifications added; emphasized the new proposal for applying holography to nonsupersymmetric gauge theory; (v4) modified the arguments about holography; (v5) minor corrections, version appeared in PRD

In order to understand thermodynamical properties of N D-branes with chemical potentials associated with R-symmetry charges, we study a one dimensional large N gauge theory (bosonic BFSS type model) as a first step. This model is obtained through a dimensional reduction of a 1+D dimensional SU(N) Yang-Mills theory and we use a 1/D expansion to investigate the phase structure. We find three phases in the \mu-T plane. We also show that all the adjoint scalars condense at large D and obtain a mass dynamically. This dynamical mass protects our model from the usual perturbative instability of massless scalars in a non-zero chemical potential. We find that the system is at least meta-stable for arbitrary large values of the chemical potentials in D \to \infty limit. We also explore the existence of similar condensation in higher dimensional gauge theories in a high temperature limit. In 2 and 3 dimensions, the condensation always happens as in one dimensional case. On the other hand, if the dimension is higher than 4, there is a critical chemical potential and the condensation happens only if the chemical potentials are below it., Comment: 37 pages, 4 figures; v2: minor corrections, references added; v3: minor corrections, to appear in JHEP