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Abstract It is shown that integrability is an accidental property of generic two-dimensional O(2)-symmetric asymptotically-free theories in the regime where the charge density is much larger than the dynamical scale. We show this by constructing an infinite tower of higher-spin conserved currents in the most generic effective Lagrangian at large chemical potential to all orders in perturbative expansion in the renormalization-group invariant coupling constant.

Abstract We apply the previously-developed sub-volume method to study the θ-dependence of the four-dimensional SU(2) Yang-Mills theory at finite temperature. We calculate the first two coefficients, the topological susceptibility χ and the fourth cumulant b 2, in the θ-expansion of the free energy density around the critical temperature (T c ) for the confinement-deconfinement transition. Lattice calculations are performed with three different spatial sizes 243 , 323 , 483 to monitor finite size effects, while the temporal size is fixed to be 8. The systematic uncertainty associated with the sub-volume extrapolation is studied with special care. The sub-volume method allows us to determine the values of b 2 much more accurately than the standard full-volume method, and we successfully identify the temperature dependence of b 2 around T c . Our numerical results suggest that the θ-dependence of the free energy density near θ = 0 changes from 4χ(1 − cos(θ/2)) to χ(1 − cos θ) as the temperature crosses T c .

We discuss the interrelations between several ideas in quantum gravity – holography, the Swampland, and the concept of ensemble averaging. To do so, we study ensemble averages of Narain-type theories associated with general even quadratic forms and their holographic duals. We establish the emergence of global symmetries and discuss their consistency with conjectures forbidding such symmetries. We also discuss how the spectral decomposition of Narain partition functions suggests a natural embedding of ensemble averaging within the low-energy limit of certain string compactifications, which in turn allows a connection with the Swampland program.

Cell-penetrating peptides (CPPs) can enter the cytosol of eukaryotic cells without killing them whereas some CPPs exhibit antimicrobial activity against bacterial cells. Here, to elucidate the mode of interaction of the CPP nona-arginine (R9) with bacterial cells, we investigated the interactions of lissamine rhodamine B red-labeled peptide (Rh-R9) with single Escherichia coli cells encapsulating calcein using confocal laser scanning microscopy. After Rh-R9 induced the leakage of a large amount of calcein, the fluorescence intensity of the cytosol due to Rh-R9 greatly increased, indicating that Rh-R9 induces cell membrane damage, thus allowing entry of a significant amount of Rh-R9 into the cytosol. To determine if the lipid bilayer region of the membrane is the main target of Rh-R9, we then investigated the interaction of Rh-R9 with single giant unilamellar vesicles (GUVs) comprising an E. coli polar lipid extract containing small GUVs and AlexaFluor 647 hydrazide (AF647) in the lumen. Rh-R9 entered the GUV lumen without inducing AF647 leakage, but leakage eventually did occur, indicating that GUV membrane damage was induced after the entry of Rh-R9 into the GUV lumen. The Rh-R9 peptide concentration dependence of the fraction of entry of Rh-R9 after a specific interaction time was similar to that of the fraction of leaking GUVs. These results indicate that Rh-R9 can damage the lipid bilayer region of a cell membrane, which may be related to its antimicrobial activity.

Abstract We study the counting problem of BPS D-branes wrapping holomorphic cycles of a general toric Calabi-Yau manifold. We evaluate the Jeffrey-Kirwan residues for the flavoured Witten index for the supersymmetric quiver quantum mechanics on the worldvolume of the D-branes, and find that BPS degeneracies are described by a statistical mechanical model of crystal melting. For Calabi-Yau threefolds, we reproduce the crystal melting models long known in the literature. For Calabi-Yau fourfolds, however, we find that the crystal does not contain the full information for the BPS degeneracy and we need to explicitly evaluate non-trivial weights assigned to the crystal configurations. Our discussions treat Calabi-Yau threefolds and fourfolds on equal footing, and include discussions on elliptic and rational generalizations of the BPS states counting, connections to the mathematical definition of generalized Donaldson-Thomas invariants, examples of wall crossings, and of trialities in quiver gauge theories.

Lattice non-invertible symmetries have rich fusion structures and play important roles in understanding various exotic topological phases. In this paper, we explore methods to generate new lattice non-invertible transformations/symmetries from a given non-invertible seed transformation/symmetry. The new lattice non-invertible symmetry is constructed by composing the seed transformations on different sites or sandwiching a unitary transformation between the transformations on the same sites. In addition to known non-invertible symmetries with fusion algebras of Tambara-Yamagami $\mathbb Z_N×\mathbb Z_N$ type, we obtain a new non-invertible symmetry in models with $\mathbb Z_N$ dipole symmetries. We name the latter the dipole Kramers-Wannier symmetry because it arises from gauging the dipole symmetry. We further study the dipole Kramers-Wannier symmetry in depth, including its topological defect, its anomaly and its associated generalized Kennedy-Tasaki transformation.

Abstract We study the Gauge/Bethe correspondence for two-dimensional N $$ \mathcal{N} $$ = (2, 2) supersymmetric quiver gauge theories associated with toric Calabi-Yau three-folds, whose BPS algebras have recently been identified as the quiver Yangians. We start with the crystal representations of the quiver Yangian, which are placed at each site of the spin chain. We then construct integrable models by combining the single-site crystals into crystal chains by a coproduct of the algebra, which we determine by a combination of representation-theoretical and gauge-theoretical arguments. For non-chiral quivers, we find that the Bethe ansatz equations for the crystal chain coincide with the vacuum equation of the quiver gauge theory, thus confirming the corresponding Gauge/Bethe correspondence. For more general chiral quivers, however, we find obstructions to the R-matrices satisfying the Yang-Baxter equations and the unitarity conditions, and hence to their corresponding Gauge/Bethe correspondence. We also discuss trigonometric (quantum toroidal) versions of the quiver BPS algebras, which correspond to three-dimensional N $$ \mathcal{N} $$ = 2 gauge theories and arrive at similar conclusions. Our findings demonstrate that there are important subtleties in the Gauge/Bethe correspondence, often overlooked in the literature.

Abstract The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce trigonometric and elliptic analogues of quiver Yangians, which we call toroidal quiver algebras and elliptic quiver algebras, respectively. We construct the representations of the shifted toroidal and elliptic algebras in terms of the statistical model of crystal melting. We also derive the algebras and their representations from equivariant localization of three-dimensional N $$ \mathcal{N} $$ = 2 supersymmetric quiver gauge theories, and their dimensionally-reduced counterparts. The analysis of supersymmetric gauge theories suggests that there exist even richer classes of algebras associated with higher-genus Riemann surfaces and generalized cohomology theories.

We explore non-invertible symmetries in two-dimensional lattice models with subsystem $\mathbb Z_2$ symmetry. We introduce a subsystem $\mathbb Z_2$-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation. The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.

We consider dark sector scenarios where dark matter is accompanied by a dark photon and multiple-flavor dark fermions charged under the dark gauge group. We study quantum interference effects in dark sector jets, where multiple dark photons are emitted from high-energy dark fermions. We perform fully quantum simulations of dark sector showers and compare the results against those of the classical Monte-Carlo simulations. We find important differences in probability distributions of dark photon countings between quantum and classical computations. When the number of dark-fermion flavors is large, we find significant enhancements in large numbers of dark photon emissions. Such enhancements can provide distinguishing signals for our scenarios at particle colliders.

Abstract We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[ T $$ \mathcal{T} $$ rank 0], to a (2+1)D interacting N $$ \mathcal{N} $$ = 4 superconformal field theory (SCFT) T $$ \mathcal{T} $$ rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = max α (− log| S 0 α + $$ {S}_{0\alpha}^{\left(+\right)} $$ |) = max α (− log| S 0 α − $$ {S}_{0\alpha}^{\left(-\right)} $$ |), where F is the round three-sphere free energy of T $$ \mathcal{T} $$ rank 0 and S 0 α ± $$ {S}_{0\alpha}^{\left(\pm \right)} $$ is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log 5 − 5 10 $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal N $$ \mathcal{N} $$ = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

Abstract We introduce a class of new algebras, the shifted quiver Yangians, as the BPS algebras for type IIA string theory on general toric Calabi-Yau three-folds. We construct representations of the shifted quiver Yangian from general subcrystals of the canonical crystal. We derive our results via equivariant localization for supersymmetric quiver quantum mechanics for various framed quivers, where the framings are determined by the shape of the subcrystals. Our results unify many known BPS state counting problems, including open BPS counting, non-compact D4-branes, and wall crossing phenomena, simply as different representations of the shifted quiver Yangians. Furthermore, most of our representations seem to be new, and this suggests the existence of a zoo of BPS state counting problems yet to be studied in detail.

Abstract We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form Q. We provide evidence that the holographic dual after the ensemble average is the three-dimensional Abelian Chern-Simons theory with kinetic term determined by Q. The resulting partition function can be written as a modular form, expressed as a sum over the partition functions of Chern-Simons theories on lens spaces. For odd lattices, the dual bulk theory is a spin Chern-Simons theory, and we identify several novel phenomena in this case. We also discuss the holographic duality prior to averaging in terms of Maxwell-Chern-Simons theories.

ABSTRACT Antimicrobial peptides (AMPs) inhibit the proliferation of or kill bacterial cells. To measure these activities, several methods have been used, which provide only the average value of many cells. Here, we report the development of a method to examine the antimicrobial and bactericidal activities of AMPs at the single-cell level (i.e., single-cell analysis) and apply this strategy to examine the interaction of an AMP, magainin 2 (Mag), with Escherichia coli cells. Using this method, we monitored the proliferation of single cells on agar in a microchamber and measured the distribution of the number of cells in each microcolony using optical microscopy. For method A, we incubated cells in the presence of various concentrations of AMPs for 3 h. The fraction of microcolonies containing only a single cell, Psingle, increased with the Mag concentration and reached 1 at a specific concentration, which corresponded to the MIC. For method B, after the interaction of a cell suspension with an AMP for a specific time, an aliquot was diluted to stop the interaction, and the proliferation of single cells then was monitored after a 3-h incubation; this method permits the definition of Psingle(t), the fraction of dead cells after the interaction. For the interaction of Mag with E. coli cells, Psingle(t) increased with the interaction time, reaching ~1 at 10 and 20 min for 25 and 13 μM Mag, respectively. Thus, these results indicate that a short interaction time between Mag and E. coli cells is sufficient to induce bacterial cell death. IMPORTANCE To elucidate the activity of antimicrobial peptides (AMPs) against bacterial cells, it is important to estimate the interaction time that is sufficient to induce cell death. We have developed a method to examine the antimicrobial and bactericidal activities of AMPs at the single-cell level (i.e., single-cell analysis). Using this method, we monitored the proliferation of single cells on agar in a microchamber and measured the distribution of the number of cells in each microcolony using optical microscopy. We found that during the interaction of magainin 2 (Mag) with E. coli cells, the fraction of dead cells, Psingle(t), increased with the interaction time, rapidly reaching 1 (e.g., 10 min for 25 μM Mag). This result indicates that Mag induces cell death after a short time of interaction.

Abstract We study θ dependence of the vacuum energy for the 4d SU(2) pure Yang-Mills theory by lattice numerical simulations. The response of topological excitations to the smearing procedure is investigated in detail, in order to extract topological information from smeared gauge configurations. We determine the first two coefficients in the θ expansion of the vacuum energy, the topological susceptibility χ and the first dimensionless coefficient b 2, in the continuum limit. We find consistency of the SU(2) results with the large N scaling. By analytic continuing the number of colors, N , to non-integer values, we infer the phase diagram of the vacuum structure of SU(N) gauge theory as a function of N and θ. Based on the numerical results, we provide quantitative evidence that 4d SU(2) Yang-Mills theory at θ = π is gapped with spontaneous breaking of the CP symmetry.

Abstract We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau threefold, the D-branes wrapping holomorphic cycles represent the BPS states, and the fixed points of the moduli spaces of BPS states are described by statistical configurations of crystal melting. Our algebras are “bootstrapped” from the molten crystal configurations, hence they act on the BPS states. We discuss the truncation of the algebra and its relation with D4-branes. We illustrate our results in many examples, with and without compact 4-cycles.

We propose a subvolume method to study the θ dependence of the free energy density of the four-dimensional SU(N) Yang-Mills theory on the lattice. As an attempt, the method is first applied to SU(2) Yang-Mills theory at T=1.2Tc to understand the systematics of the method. We then proceed to the calculation of the vacuum energy density and obtain the θ dependence qualitatively different from the high temperature case. The numerical results combined with the theoretical requirements provide the evidence for the spontaneous CP violation at θ=π, which is in accordance with the large N prediction and indicates that the similarity between 4d SU(N) and 2d CPN−1 theories does not hold for N=2.

Abstract We study a perturbative expansion of the squashed 3-sphere s b 3 $$ \left({s}_b^3\right) $$ partition function of 3d N $$ \mathcal{N} $$ = 2 gauge theories around the squashing parameter b = 1. Our proposal gives the coefficients of the perturbative expansion as a finite sum over the saddle points of the supersymmetric-localization integral in the limit b → 0 (the so-called Bethe vacua), and the contribution from each Bethe vacua can be systematically computed using saddle-point methods. Our expansion provides an efficient and practical method for computing basic CFT data (F, C T , C JJ and higher-point correlation functions of the stress-energy tensor) of the IR superconformal field theory without performing the localization integrals.

Abstract It has recently pointed out that a four-dimensional analog of Chern-Simons theory provides an elegant framework for understanding integrable models with spectral parameters. The goal of this short note is to better understand the relation of this theory to the more standard three-dimensional Chern-Simons theory. We point out that two Chern-Simons theories, in four dimensions and three dimensions, are related by a novel T-duality in field theory. We then discuss this T-duality in string theory. Our T-duality prescription applies to a more general class of topological quantum field theories, producing mixed topological/holomorphic theories. This paper is motivated by the observation by C. Vafa.

Scalar weak gravity conjectures (SWGCs) attempt to pinpoint the ranges of couplings consistent with a fundamental theory of all interactions. We identify a generic dynamical consequence of these conjectures for cosmology and show that SWGCs imply a particular behavior of the scalar fields in the early universe. A scalar field that develops a large expectation value during inflation must relax to the minimum of effective potential at a later time. SWGCs imply that a homogeneous distribution of the field is unstable with respect to fragmentation into localized lumps, which could potentially lead to significant consequences for cosmology.

Abstract A low-energy effective theory is said to be in the swampland if it does not have any consistent UV completion inside a theory of quantum gravity. The natural question is if the standard model of particle physics, possibly with some minimal extensions, are in the swampland — we are in trouble if the answer to this question is yes. We discuss this question in view of the recent swampland conjectures. We prove a no-go theorem concerning the modification of the Higgs sector. Moreover, we find that QCD axion is incompatible with the recent swampland conjectures, unless some sophisticated possibilities are considered. We discuss the implications of this result for spontaneous breaking of CP symmetry. We comment on dynamical supersymmetry breaking as well as the issue of multi-valuedness of the potential. We also propose a refinement of the de Sitter swampland conjecture.

Abstract It has recently been shown that a center-twisted compactification of the four-dimensional pure SU(N) Yang-Mills theory on a three-torus gives rise to the twodimensional ℂℙ N− 1-model on a circle with a flavor-twisted boundary condition. We verify the consistency of this statement non-perturbatively at theta angle θ = π, in terms of the mixed ’t Hooft anomalies for flavor symmetries and the time-reversal symmetry. This provides further support for the approach to the confinement of four-dimensional Yang-Mills theory from the two-dimensional ℂℙ N− 1-model.

We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang–Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang–Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.

We point out that a simple inflationary model in which the axionic inflaton couples to a pure Yang–Mills theory may give the scalar spectral index (ns) and tensor-to-scalar ratio (r) in complete agreement with the current observational data.

Abstract We study four-dimensional SU(N) Yang-Mills theory on ℝ × T 3 = ℝ × S A 1 × S B 1 × S C 1 $$ \mathbb{R}\times {\mathbb{T}}^3=\mathbb{R}\times {S}_A^1\times {S}_B^1\times {S}_C^1 $$ , with a twisted boundary condition by a ℤ N center symmetry imposed on S B 1 × S C 1 . This setup has no IR zero modes and hence is free from IR divergences which could spoil trans-series expansion for physical observables. Moreover, we show that the center symmetry is preserved at weak coupling regime. This is shown by first reducing the theory on T 2 = S A × S B $$ {\mathbb{T}}^2={S}_A\times {S}_B $$ , to connect the model to the two-dimensional ℂℙ N− 1-model. Then, we prove that the twisted boundary condition by the center symmetry for the Yang-Mills is reduced to the twisted boundary condition by the ℤ N global symmetry of ℂℙ N− 1. There are N classical vacua, and fractional instantons connecting those N vacua dynamically restore the center symmetry. We also point out the presence of singularities on the Borel plane which depend on the shape of the compactification manifold, and comment on its implications.

Abstract We define “BPS graphs” on punctured Riemann surfaces associated with A N −1 theories of class S $$ \mathcal{S} $$ . BPS graphs provide a bridge between two powerful frameworks for studying the spectrum of BPS states: spectral networks and BPS quivers. They arise from degenerate spectral networks at maximal intersections of walls of marginal stability on the Coulomb branch. While the BPS spectrum is ill-defined at such intersections, a BPS graph captures a useful basis of elementary BPS states. The topology of a BPS graph encodes a BPS quiver, even for higher-rank theories and for theories with certain partial punctures. BPS graphs lead to a geometric realization of the combinatorics of Fock-Goncharov N - triangulations and generalize them in several ways.

We propose a mechanism for confinement: analytic continuation beyond infinite coupling in the space of the coupling constant. The analytic continuation is realized by renormalization group flows from the weak to the strong coupling regime. We demonstrate this mechanism explicitly for the mass gap in two-dimensional σ models in the large N limit. Our analysis suggests that the conventional analysis of the operator product expansion in itself does not necessarily guarantee the existence of a classical solution corresponding to renormalons. We discuss how the renormalon puzzle may be resolved by the analytic continuation beyond infinite coupling.