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We study particular integrated correlation functions of two superconformal primary operators of the stress tensor multiplet in the presence of a half-BPS line defect labelled by electromagnetic charges (p, q) in N = 4 supersymmetric Yang-Mills theory (SYM) with gauge group SU(N). An important consequence of SL(2, ℤ) electromagnetic duality in N = 4 SYM is that correlators of line defect operators with different charges (p, q) must be related in a non-trivial manner when the complex coupling τ = θ/(2π) + 4 πi / g YM 2 is transformed appropriately. In this work we introduce a novel class of real-analytic functions whose automorphic properties with respect to SL(2, ℤ) match the expected transformations of line defect operators in N = 4 SYM under electromagnetic duality. At large N and fixed τ, the correlation functions we consider are related to scattering amplitudes of two gravitons from extended (p, q)-strings in the holographic dual type IIB superstring theory. We show that the large-N expansion coefficients of the integrated two-point line defect correlators are given by finite linear combinations with rational coefficients of elements belonging to this class of automorphic functions. On the other hand, for any fixed value of N we conjecture that the line defect integrated correlators can be expressed as formal infinite series over such automorphic functions. The resummation of this series produces a simple lattice sum representation for the integrated line defect correlator that manifests its automorphic properties. We explicitly demonstrate this construction for the cases with gauge group SU(2) and SU(3). Our results give direct access to non-perturbative integrated correlators in the presence of an ’t Hooft-line defect, observables otherwise very difficult to compute by other means. [ABSTRACT FROM AUTHOR]

We study 't Hooft lines in four-dimensional holomorphic-topological Chern-Simons theory. We relate them to Q-operators in the theory of integrable systems. We give a physical interpretation of the fundamental TQ and QQ relations satisfied by Q-operators and conventional transfer matrices. [ABSTRACT FROM AUTHOR]

In the production of cyclohexene by benzene hydrogenation, the by-product cyclohexane forms an azeotrope with cyclohexene. For the extraction and distillation of the binary azeotrope (cyclohexene + cyclohexane), the selectivity and relative volatility of 24 different entrainers were compared and the intermolecular interaction forces and interaction energies were analyzed by the DMol3 module of Materials Studio (MS). N, N-dimethylformamide (DMF) was identified as the entrainer, and vapour–liquid equilibrium (VLE) data were measured at atmospheric pressure for the binary system {cyclohexane + cyclohexene} with a temperature range of 354 K to 356 K, the binary system {cyclohexane + DMF} with a temperature range of 354 K to 390 K, and the binary system {cyclohexene + DMF} with a temperature range of 357 K to 421 K. In addition, the thermodynamic consistency of the experimental data was checked using the Wisniak and Van Ness method. The Wilson, NRTL, and UNIQUAC models were used to regress and fit the experimental data to optimize the binary interaction parameters, and the root mean square (RMSD) and average absolute deviation (AAD) values of all models were below 0.01%, indicating that the experimental data provide a basis for the simulation and optimization of the extractive distillation process. [ABSTRACT FROM AUTHOR]

Abstract We study particular integrated correlation functions of two superconformal primary operators of the stress tensor multiplet in the presence of a half-BPS line defect labelled by electromagnetic charges (p, q) in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory (SYM) with gauge group SU(N). An important consequence of SL(2, ℤ) electromagnetic duality in N $$ \mathcal{N} $$ = 4 SYM is that correlators of line defect operators with different charges (p, q) must be related in a non-trivial manner when the complex coupling τ = θ/(2π) + 4 πi / g YM 2 $$ 4\pi i/{g}_{\textrm{YM}}^2 $$ is transformed appropriately. In this work we introduce a novel class of real-analytic functions whose automorphic properties with respect to SL(2, ℤ) match the expected transformations of line defect operators in N $$ \mathcal{N} $$ = 4 SYM under electromagnetic duality. At large N and fixed τ, the correlation functions we consider are related to scattering amplitudes of two gravitons from extended (p, q)-strings in the holographic dual type IIB superstring theory. We show that the large-N expansion coefficients of the integrated two-point line defect correlators are given by finite linear combinations with rational coefficients of elements belonging to this class of automorphic functions. On the other hand, for any fixed value of N we conjecture that the line defect integrated correlators can be expressed as formal infinite series over such automorphic functions. The resummation of this series produces a simple lattice sum representation for the integrated line defect correlator that manifests its automorphic properties. We explicitly demonstrate this construction for the cases with gauge group SU(2) and SU(3). Our results give direct access to non-perturbative integrated correlators in the presence of an ’t Hooft-line defect, observables otherwise very difficult to compute by other means.

Abstract We study ’t Hooft lines in four-dimensional holomorphic-topological Chern-Simons theory. We relate them to Q-operators in the theory of integrable systems. We give a physical interpretation of the fundamental TQ and QQ relations satisfied by Q-operators and conventional transfer matrices.

Abstract Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on average. This work investigates the constraints on mixed states resulting from non-commuting average symmetries. We will focus on the cases where the commutation relations of the average symmetry generators are violated by nontrivial phases, and call such average symmetry anomalous. We show that anomalous average symmetry implies degeneracy in the density matrix eigenvalues, and present several lattice examples with average symmetries, including XY chain, Heisenberg chain, and deformed toric code models. In certain cases, the results can be further extended to reduced density matrices, leading to a new lower bound on the entanglement entropy. We discuss several applications in the contexts of many body localization, quantum channels, entanglement phase transitions and also derive new constraints on the Lindbladian evolution of open quantum systems.

Abstract We consider the complete set of planar two-loop five-point Feynman integrals with two off-shell external legs. These integrals are relevant, for instance, for the calculation of the second-order QCD corrections to the production of two heavy vector bosons in association with a jet or a photon at a hadron collider. We construct pure bases for these integrals and reconstruct their analytic differential equations in canonical form through numerical sampling over finite fields. The newly identified symbol alphabet, one of the most complex to date, provides valuable data for bootstrap methods. We then apply our results to initiate the study of double Lagrangian insertions in a four-cusp Wilson loop in planar maximally supersymmetric Yang-Mills theory, computing it through two loops. We observe that it is finite, conformally invariant in four dimensions, and of uniform transcendentality. Furthermore, we provide numerical evidence for its positivity within the amplituhedron region through two loops.

Abstract Starting from the Lorentzian inversion formula, we derive a dispersion relation which computes a four-point function in 1d CFTs as an integral over its double discontinuity. The crossing symmetric kernel of the integral is given explicitly for the case of identical operators with integer or half-integer scaling dimension. This derivation complements the one that uses analytic functionals. We use the dispersion relation to evaluate holographic correlators defined on the half-BPS Wilson line of planar N $$ \mathcal{N} $$ = 4 super Yang-Mills, reproducing results up to fourth order in an expansion at large t’Hooft coupling.

Abstract The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ 3, ζ 5 to the cusp anomalous dimension.

Abstract We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.

Abstract We compute the tree-level connected six-point function of identical scalar fluctuations of the AdS2 string worldsheet dual to the half-BPS Wilson line in planar N $$ \mathcal{N} $$ = 4 Super Yang-Mills. The calculation can be carried out analytically in the conformal gauge approach, where the boundary reparametrization mode of the string plays a crucial role. We also study the analytic continuation of the six-point function to an out-of-time-order configuration, which is related to a 3-to-3 scattering amplitude in flat space. As a check of our results, we also numerically compute the six-point function using the Nambu-Goto action in static gauge, finding agreement with the conformal gauge answer.

Abstract We study a 2+1D lattice gauge theory with fundamental representation scalar fields which has both Higgs and confining regimes with a spontaneously-broken U(1) 0-form symmetry. We show that the Higgs and confining regimes may be distinguished by a natural gauge invariant observable: the phase Ω of a correlation function of a vortex line operator linking with an electric Wilson line. We employ dualities and strong coupling expansions to analytically explore parameter regimes which were inaccessible in previous continuum calculations, and discuss possible implications for the phase diagram.

Abstract In this second installment of a series of two papers on the 1 2 $$ \frac{1}{2} $$ -BPS Wilson line defect CFT in N $$ \mathcal{N} $$ = 4 super Yang-Mills, we focus on dynamical aspects of the theory, in particular studying four-point functions with analytic bootstrap methods. Relying on the results of [1] for the kinematics and strong coupling spectrum, we consider various four-point functions in the planar limit, in an expansion for large ’t Hooft coupling. Our ultimate goal is to provide a detailed derivation of the four-point function of the displacement supermultiplet at three loops, first presented in [2]. Along the way, we present a large amount of new results including four-point functions with zero, one or two long external supermultiplets. The last two represent a novelty in the analytic bootstrap literature and are instrumental in addressing the problem of operators degeneracy. Such phenomenon leads to the necessity of resolving a mixing problem that is more complicated than those usually encountered in the study of holographic correlators, thus leading us to the development of a new approach that we believe will have a wider range of applicability. Related to this issue, we analyze in some detail the structure of the dilatation operator in this model. Some of the ingredients that we use apply more generally to holographic theories, although a thorough investigation of these aspects is missing, to the best of our knowledge, in most interesting cases.

Abstract We study the Wilson line defect half-indices of 3d N $$ \mathcal{N} $$ = 2 supersymmetric SU(N) Chern-Simons theories of level k ≤ – N with Neumann boundary conditions for the gauge fields, together with 2d Fermi multiplets and fundamental 3d chiral multiplets to cancel the gauge anomaly. We derive some exact results and also make some conjectures based on expansions of the q-series. We find several interesting connections with special functions known in the literature, including Rogers-Ramanujan functions for which we conjecture integral representations, and the appearance of Appell-Lerch sums for certain Wilson line half-index grand canonical ensembles which reveal an unexpected appearance of mock modular functions. We also find intriguing q-difference equations relating half-indices to Wilson line half-indices. Some of these results also have a description in terms of a dual theory with Dirichlet boundary conditions for the vector multiplet in the dual theory.

We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed. [ABSTRACT FROM AUTHOR]

We study a 2+1D lattice gauge theory with fundamental representation scalar fields which has both Higgs and confining regimes with a spontaneously-broken U(1) 0-form symmetry. We show that the Higgs and confining regimes may be distinguished by a natural gauge invariant observable: the phase Ω of a correlation function of a vortex line operator linking with an electric Wilson line. We employ dualities and strong coupling expansions to analytically explore parameter regimes which were inaccessible in previous continuum calculations, and discuss possible implications for the phase diagram. [ABSTRACT FROM AUTHOR]

In this second installment of a series of two papers on the 1 2 -BPS Wilson line defect CFT in N = 4 super Yang-Mills, we focus on dynamical aspects of the theory, in particular studying four-point functions with analytic bootstrap methods. Relying on the results of [1] for the kinematics and strong coupling spectrum, we consider various four-point functions in the planar limit, in an expansion for large ’t Hooft coupling. Our ultimate goal is to provide a detailed derivation of the four-point function of the displacement supermultiplet at three loops, first presented in [2]. Along the way, we present a large amount of new results including four-point functions with zero, one or two long external supermultiplets. The last two represent a novelty in the analytic bootstrap literature and are instrumental in addressing the problem of operators degeneracy. Such phenomenon leads to the necessity of resolving a mixing problem that is more complicated than those usually encountered in the study of holographic correlators, thus leading us to the development of a new approach that we believe will have a wider range of applicability. Related to this issue, we analyze in some detail the structure of the dilatation operator in this model. Some of the ingredients that we use apply more generally to holographic theories, although a thorough investigation of these aspects is missing, to the best of our knowledge, in most interesting cases. [ABSTRACT FROM AUTHOR]

We study the Wilson line defect half-indices of 3d N = 2 supersymmetric SU(N) Chern-Simons theories of level k ≤ – N with Neumann boundary conditions for the gauge fields, together with 2d Fermi multiplets and fundamental 3d chiral multiplets to cancel the gauge anomaly. We derive some exact results and also make some conjectures based on expansions of the q-series. We find several interesting connections with special functions known in the literature, including Rogers-Ramanujan functions for which we conjecture integral representations, and the appearance of Appell-Lerch sums for certain Wilson line half-index grand canonical ensembles which reveal an unexpected appearance of mock modular functions. We also find intriguing q-difference equations relating half-indices to Wilson line half-indices. Some of these results also have a description in terms of a dual theory with Dirichlet boundary conditions for the vector multiplet in the dual theory. [ABSTRACT FROM AUTHOR]

Abstract This is the first of a series of two papers in which we study the one-dimensional defect CFT defined by insertions of local operators along a $$\frac{1}{2}$$ -BPS Wilson line in $$\mathcal{N}$$ = 4 super Yang-Mills. In this first paper we focus on the kinematical implications of invariance under the $$\mathfrak{o}\mathfrak{s}\mathfrak{p}\left({4}^{*}|4\right)$$ superconformal algebra preserved by the line. We study correlation functions involving both protected and unprotected supermultiplets and derive the associated superconformal blocks, using two types of superspace for short and long representations. We also discuss the spectrum of defect theories defined by the Wilson line, focusing in particular on fundamental lines in the planar limit: in this case we provide a detailed analysis of the type and number of states both at weak ’t Hooft coupling, via the free gauge theory description of the defect CFT, and at strong coupling, where there is a dual description via AdS/CFT. Focusing on the strongly-coupled regime, which will be subject to a detailed analysis using analytic bootstrap techniques in [1], we also develop a strategy that allows to explicitly build superconformal primary operators and their superconformal descendants in terms of the elementary fields in the AdS Lagrangian description. The explicit results will be used in [1] to address the problem of operators mixing at strong coupling. This paper and the companion [1] provide an extended version of the results presented in [2].

This is the first of a series of two papers in which we study the one-dimensional defect CFT defined by insertions of local operators along a -BPS Wilson line in = 4 super Yang-Mills. In this first paper we focus on the kinematical implications of invariance under the superconformal algebra preserved by the line. We study correlation functions involving both protected and unprotected supermultiplets and derive the associated superconformal blocks, using two types of superspace for short and long representations. We also discuss the spectrum of defect theories defined by the Wilson line, focusing in particular on fundamental lines in the planar limit: in this case we provide a detailed analysis of the type and number of states both at weak ’t Hooft coupling, via the free gauge theory description of the defect CFT, and at strong coupling, where there is a dual description via AdS/CFT. Focusing on the strongly-coupled regime, which will be subject to a detailed analysis using analytic bootstrap techniques in [1], we also develop a strategy that allows to explicitly build superconformal primary operators and their superconformal descendants in terms of the elementary fields in the AdS Lagrangian description. The explicit results will be used in [1] to address the problem of operators mixing at strong coupling. This paper and the companion [1] provide an extended version of the results presented in [2]. [ABSTRACT FROM AUTHOR]

Abstract The open string dual to a 1/6 BPS Wilson line in the N $$ \mathcal{N} $$ = 6 super Chern-Simons-matter theory is coupled to a flat Kalb-Ramond field. We show that the resulting boundary term imposes mixed boundary conditions on the fields that describe the fluctuations on the world-sheet. These boundary conditions fix a combination of the derivatives of the fluctuations, parallel and transverse to the boundary. We holographically compute the correlation functions of insertions on the Wilson line in terms of world-sheet Witten diagrams. We observe that their functional dependence is consistent with the conformal symmetry on the line.

The neuron can be referred to as the primary cell of the nervous system, responsible for transmitting messages through electrical signals between neurons or other cells. To comprehend the intricate behavior of neuron performance, a set of differential equations incorporating non-linear functions is necessary. This research introduces a novel method to improve the digital implementation of Wilson and Morris-Lecar neuron models, offering multiple benefits such as decreased hardware needs, enhanced processing speed and accuracy, and reduced implementation expenses. The proposed method simplifies the original model by converting all its differential equations into a single trigonometric function. This transformation greatly reduces computational complexity by eliminating the need for multipliers, resulting in a concise set of mathematical expressions. The digital implementation of this innovative approach can be efficiently achieved using the COordinate Rotation DIgital Computer (CORDIC) algorithm, which avoids the need for complex mathematical operations. To showcase the effectiveness of this approach, the suggested model is synthesized and implemented on a Field-Programmable Gate Array (FPGA) with successful results. The implementation outcomes reveal a significant improvement in operational frequency, approximately 3.28 and 4.68 times (for Wilson and Morris-Lecar, respectively) higher than the original model.

Abstract We study the large N and large representation limits of the Schur line defect correlators of the Wilson line operators transforming in the (anti)symmetric, hook and rectangular representations for 𝒩 = 4 U(N) super Yang-Mills theory. By means of the factorization property, the large N correlators of the Wilson line operators in arbitrary representations can be exactly calculated in principle. In the large representation limit they turn out to be expressible in terms of certain infinite series such as Ramanujan’s general theta functions and the q-analogues of multiple zeta values (q-MZVs). Several generating functions for combinatorial objects, including partitions with non-negative cranks and conjugacy classes of general linear groups over finite fields, emerge from the large N correlators. Also we find conjectured properties of the automorphy and the hook-length expansion satisfied by the large N correlators.

The open string dual to a 1/6 BPS Wilson line in the N = 6 super Chern-Simons-matter theory is coupled to a flat Kalb-Ramond field. We show that the resulting boundary term imposes mixed boundary conditions on the fields that describe the fluctuations on the world-sheet. These boundary conditions fix a combination of the derivatives of the fluctuations, parallel and transverse to the boundary. We holographically compute the correlation functions of insertions on the Wilson line in terms of world-sheet Witten diagrams. We observe that their functional dependence is consistent with the conformal symmetry on the line. [ABSTRACT FROM AUTHOR]

Disputes over legal jurisdiction in Canada predate its own Constitution. Even after the 1982 repatriation of the Constitution, First Nations governance remains entangled in a jurisdictional divide. In the spirit of Indigenous self-determination, this article argues the impracticality of First Nations regulating themselves according to federal employment standards under the Canada Labour Code1 in preference of provincial or territorial standards. A review of jurisprudence since NIL/TU,O underscores the inconsistency of trial division and appellate courts across Canada in determining the appropriate jurisdiction for employment law issues in First Nations communities. This incoherence leaves First Nations communities in a precarious position in regulating employment. An employer’s ability to consistently depend on the provincial and territorial regimes is imperative given the innumerable barriers already facing First Nations communities, particularly in an area of law where federal regulation is increasingly convoluted, for example by the Supreme Court of Canada in Wilson. Counter-intuitive as it may seem, the otherwise far more generous federal employment standards have the effect of eroding the autonomy necessary for First Nations’ self-determination. [ABSTRACT FROM AUTHOR]

Wilson's disease is a complicated medical condition caused by the accumulation of copper, mostly in the liver and brain. The genetic basis of Wilson's disease is attributed to the presence of pathogenic variants in the ATP7B copper-transporting gene, which prevents the excretion of copper through the biliary tract. To date, ATP7B remains the only identified gene that has been linked to the development of this disease. Our understanding of the disease has been associated with the identification of particular disease-causing variants that present specific impairments in copper transporters. It is crucial to identify the most frequent variant in terms of ethnicity to facilitate testing of its functionality. This study represents the initial comprehensive analysis of ATP7B variants, providing insights into the extensive range of disease-causing mutations. Here, we describe the 1275 distinct ATP7B variants documented so far, with particular emphasis on their regional and ethnic prevalence. The H1069Q missense variant is the most frequently reported in Europe, Northern America, and North Africa, whereas the R778L, C271*, and M645R variants are the most prevalent in the East Asian, Middle Eastern-South Asian, and South American populations, respectively. Acquiring such knowledge would facilitate the implementation of a selective mutation screening approach, targeting the most predominant variant identified within a specific ethnic group or geographic region for better diagnosis of the disease.

In this paper, I will argue against certain criticisms of Kripke’s Wittgenstein’s sceptical argument and sceptical solution, made especially by Baker and Hacker, McGinn, and McDowell. I will show that their interpretation of Kripke’s Wittgenstein’s view is misplaced. According to Kripke’s Wittgenstein’s sceptical argument, there is no fact as to what someone means by her words. For Kripke, this conclusion, combined with Classical Realist view of meaning, leads to the Wittgensteinian paradox, according to which there is no such thing as meaning anything by any word. Wittgenstein presents this paradox in paragraph 201 of the Philosophical Investigations. As Kripke reads Wittgenstein, Wittgenstein is in agreement with his sceptic on the sceptical conclusion of the sceptical argument, that is, that there is no fact about meaning, and builds his sceptical solution on an endorsement of that. McDowell, McGinn, and others have objected that Kripke has failed to properly understand Wittgenstein’s main remarks in 201, that is, that the paradox is the result of a misunderstanding of the ordinary notion of meaning. Wittgenstein does not accept such a sceptical conclusion. I will use the distinction George Wilson draws between two different conclusions of the sceptical argument and show that Kripke has respected all of the remarks that Wittgenstein has put in section 201.

Abstract Theories with compact extra dimensions can exhibit a vacuum instability known as a bubble of nothing. These decay modes can be obstructed if the internal manifold is stabilized by fluxes, or if it carries Wilson lines for background gauge fields, or if the instanton is incompatible with the spin structure. In each of these cases the decay can proceed by adding dynamical charged membranes or gauge fields. We give a general, bottom-up procedure for constructing approximate bubble of nothing solutions in models with internal spheres stabilized by flux and study the influence of the brane tension on the tunneling exponent, finding two branches of solutions that merge at a minimal superextremal value of the tension. In the case of Wilson operators and incompatible fermions, the relevant bubble is shown to be the Euclidean Reissner-Nordstrom black hole, and the ordinary decay exponent is modified by 1/g 2 effects. We examine the Dirac operator on this background and comment on the relevance for models of supergravity with gauged R-symmetry.

Abstract I study the two-dimensional defects of the d dimensional critical O(N) model and the defect RG flows between them. By combining the ϵ-expansion around d = 4 and d = 6 as well as large N techniques, I find new conformal defects and examine their behavior across dimensions and at various N. I discuss how some of these fixed points relate to the known ordinary, special and extraordinary transitions in the 3d theory, as well as examine the presence of new symmetry breaking fixed points preserving an O(p) × O(N − p) subgroup of O(N) for N ≤ N c (with the estimate N c = 6). I characterise these fixed points by obtaining their conformal anomaly coefficients, their 1-point functions and comment on the calculation of their string potential. These results establish surface operators as a viable approach to the characterisation of interface critical phenomena in the 3d critical O(N) model.

Abstract In this paper we initiate the study of correlation functions of a single trace operator and a circular supersymmetric Wilson loop in ABJM theory. The single trace operator is in the scalar sector and is an eigenstate of the planar two-loop dilatation operator. The Wilson loop is in the fundamental representation of the gauge group or a suitable (super-)group. Such correlation functions at tree level can be written as an overlap of the Bethe state corresponding to the single trace operator and a boundary state which corresponds to the Wilson loop. There are various type of supersymmetric Wilson loops in ABJM theory. We show that some of them correspond to tree-level integrable boundary states while some are not. For the tree-level integrable ones, we prove their integrability and obtain analytic formula for the overlaps. For the non-integrable ones, we give examples of non-vanishing overlaps for Bethe states which violate selection rules.

Abstract The qq-characters are powerful tools to reveal symmetries and integrabilities of Seiberg-Witten theories. The goal of this paper is to provide analytic expressions of qq-characters based on Young diagrams in 5d 𝒩 = 1 pure Yang-Mills theories with BCD-type gauge groups, by focusing on the unrefined limit. Using these expressions, we investigate the relationships among qq-characters of classical gauge groups. For SO(n) gauge groups, we construct a quantum-toroidal-like algebra via the Ward-identity approach, which allows us to derive the qq-characters.

Abstract In this paper we use lattice simulation to study four dimensional N $$ \mathcal{N} $$ = 4 super Yang-Mills (SYM) theory. We have focused on the three color theory on lattices of size 124 and for ’t Hooft couplings up to λ = 40.0. Our lattice action is based on a discretization of the Marcus or GL twist of N $$ \mathcal{N} $$ = 4 SYM and retains one exact supersymmetry for non-zero lattice spacing. We show that lattice theory exists in a single non-Abelian Coulomb phase for all ’t Hooft couplings. Furthermore the static potential we obtain from correlators of Polyakov lines is in good agreement with that obtained from holography — specifically the potential has a Coulombic form with a coefficent that varies as the square root of the ’t Hooft coupling.

Abstract We study new 1/24 BPS circular Wilson loops in ABJ(M) theory, which are defined in terms of several parameters that continuously interpolate between previously known 1/6 BPS loops (both bosonic and fermionic) and 1/2 BPS fermionic loops. We compute the expectation value of these operators up to second order in perturbation theory using a one-dimensional effective field theory approach. Within dimensional regularization, we find non-trivial β-functions for the parameters, which are marginally relevant deformations triggering RG flows from a UV fixed point represented by the 1/6 BPS bosonic loop to an IR fixed point represented by a 1/2 BPS fermionic loop. Generically, along all flows at least one supercharge of the theory is preserved, so that we refer to them as enriched RG flows. In particular, fixed points are connected through 1/6 BPS fermionic operators. This holds at framing zero, which is a consequence of the regularization scheme employed. We also establish the validity of the g-theorem, relating the expectation values of the Wilson loops corresponding to the UV and IR fixed points of the flow, and discuss the one-dimensional defect SCFT living on the Wilson loop contour.

Abstract We present two complementary approaches to calculating the 2-point function of stress tensors in the presence of a 1/2 BPS surface defect of the 6d 𝒩 = (2, 0) theories. First, we use analytical bootstrap techniques at large N to obtain the first nontrivial correction to this correlator, from which we extract the defect CFT (dCFT) data characterising the 2d dCFT of the 1/2 BPS plane. Along the way we derive a supersymmetric inversion formula, obtain the relevant superconformal blocks and check that crossing symmetry is satisfied. Notably our result features a holomorphic function whose appearance is related to the chiral algebra construction of Beem, Rastelli and van Rees. Second, we use that chiral algebra description to obtain exact results for the BPS sector of the dCFT, valid at any N and for any choice of surface operator. These results provide a window into the dynamics of strings of the mysterious 6d theories.

Abstract We propose a mechanism that couples matter fields to three-dimensional de Sitter quantum gravity. Our construction is based on the Chern-Simons formulation of three-dimensional Euclidean gravity, and it centers on a collection of Wilson loops winding around Euclidean de Sitter space. We coin this object a Wilson spool. To construct the spool, we build novel representations of 𝔰𝔲(2). To evaluate the spool, we adapt and exploit several known exact results in Chern-Simons theory. Our proposal correctly reproduces the one-loop determinant of a free massive scalar field on S 3 as G N → 0. Moreover, allowing for quantum metric fluctuations, it can be systematically evaluated to any order in perturbation theory.

Abstract We address a longstanding question of whether ABJM theory has Wilson loop operators preserving eight supercharges (so 1/3 BPS). We present such Wilson loops made of a large supermatrix combining two 1/2 BPS Wilson loops. We study the spectrum of operator insertions into them including the displacement operator and several others and study their correlation functions. Another natural construction arising in this context are Wilson loops with alternating superconnections. This amounts to including “defect changing operators” along the loop, similar to a discrete cusp. This insertion is topological and preserves two supercharges. We study the multiplet of this operator and how it can be used to introduce further operators. We also construct the defect conformal manifold arising from marginal defect operators.

Abstract We study the integrability properties of Wilson loops in the 𝒩 = 6 three-dimensional Chern-Simons-matter (ABJM) theory. We begin with the construction of an open spin chain that describes the anomalous dimensions of operators inserted along the contour of a 1/2 BPS Wilson loop. Moreover, we compute the all-loop reflection matrices that govern the interaction of spin-chain excitations with the boundary, including their dressing factors, and we check them against weak- and strong-coupling results. Furthermore, we propose a Y -system of equations for the cusped Wilson line of ABJM, and we use it to reproduce the one-loop cusp anomalous dimension of ABJM from a leading-order finite-size correction. Finally, we write a set of BTBA equations consistent with the Y -system proposal.

Abstract We study the Schur line defect correlation functions in $$ \mathcal{N} $$ = 4 and $$ \mathcal{N} $$ = 2∗ U(N) super Yang-Mills (SYM) theory. We find exact closed-form formulae of the correlation functions of the Wilson line operators in the fundamental, antisymmetric and symmetric representations via the Fermi-gas method in the canonical and grand canonical ensembles. All the Schur line defect correlators are shown to be expressible in terms of multiple series that generalizes the Kronecker theta function. From the large N correlators we obtain generating functions for the spectra of the D5-brane giant and the D3-brane dual giant and find a correspondence between the fluctuation modes and the plane partition diamonds.

Abstract A theory with a non-compact form-symmetry is described by two closed form fields of degrees k and d – k. Effective theory examples are non-linear electrodynamics, a photon field coupled to a neutron field, and a low energy Goldstone boson. We show these models cannot be completed in the UV without breaking the non-compact form-symmetry down to a compact one. This amounts to the existence of electric or magnetic charges. A theory with an unbroken non-compact k-form symmetry is massless and free.

In this paper, I will argue against certain criticisms of Kripke's Wittgenstein's sceptical argument and sceptical solution, made especially by Baker and Hacker, McGinn, and McDowell. I will show that their interpretation of Kripke's Wittgenstein's view is misplaced. According to Kripke's Wittgenstein's sceptical argument, there is no fact as to what someone means by her words. For Kripke, this conclusion, combined with Classical Realist view of meaning, leads to the Wittgensteinian paradox, according to which there is no such thing as meaning anything by any word. Wittgenstein presents this paradox in paragraph 201 of the Philosophical Investigations. As Kripke reads Wittgenstein, Wittgenstein is in agreement with his sceptic on the sceptical conclusion of the sceptical argument, that is, that there is no fact about meaning, and builds his sceptical solution on an endorsement of that. McDowell, McGinn, and others have objected that Kripke has failed to properly understand Wittgenstein's main remarks in 201, that is, that the paradox is the result of a misunderstanding of the ordinary notion of meaning. Wittgenstein does not accept such a sceptical conclusion. I will use the distinction George Wilson draws between two different conclusions of the sceptical argument and show that Kripke has respected all of the remarks that Wittgenstein has put in section 201. [ABSTRACT FROM AUTHOR]

Theories with compact extra dimensions can exhibit a vacuum instability known as a bubble of nothing. These decay modes can be obstructed if the internal manifold is stabilized by fluxes, or if it carries Wilson lines for background gauge fields, or if the instanton is incompatible with the spin structure. In each of these cases the decay can proceed by adding dynamical charged membranes or gauge fields. We give a general, bottom-up procedure for constructing approximate bubble of nothing solutions in models with internal spheres stabilized by flux and study the influence of the brane tension on the tunneling exponent, finding two branches of solutions that merge at a minimal superextremal value of the tension. In the case of Wilson operators and incompatible fermions, the relevant bubble is shown to be the Euclidean Reissner-Nordstrom black hole, and the ordinary decay exponent is modified by 1/g2 effects. We examine the Dirac operator on this background and comment on the relevance for models of supergravity with gauged R-symmetry. [ABSTRACT FROM AUTHOR]

I study the two-dimensional defects of the d dimensional critical O(N) model and the defect RG flows between them. By combining the ϵ-expansion around d = 4 and d = 6 as well as large N techniques, I find new conformal defects and examine their behavior across dimensions and at various N. I discuss how some of these fixed points relate to the known ordinary, special and extraordinary transitions in the 3d theory, as well as examine the presence of new symmetry breaking fixed points preserving an O(p) × O(N − p) subgroup of O(N) for N ≤ Nc (with the estimate Nc = 6). I characterise these fixed points by obtaining their conformal anomaly coefficients, their 1-point functions and comment on the calculation of their string potential. These results establish surface operators as a viable approach to the characterisation of interface critical phenomena in the 3d critical O(N) model. [ABSTRACT FROM AUTHOR]

In this paper we initiate the study of correlation functions of a single trace operator and a circular supersymmetric Wilson loop in ABJM theory. The single trace operator is in the scalar sector and is an eigenstate of the planar two-loop dilatation operator. The Wilson loop is in the fundamental representation of the gauge group or a suitable (super-)group. Such correlation functions at tree level can be written as an overlap of the Bethe state corresponding to the single trace operator and a boundary state which corresponds to the Wilson loop. There are various type of supersymmetric Wilson loops in ABJM theory. We show that some of them correspond to tree-level integrable boundary states while some are not. For the tree-level integrable ones, we prove their integrability and obtain analytic formula for the overlaps. For the non-integrable ones, we give examples of non-vanishing overlaps for Bethe states which violate selection rules. [ABSTRACT FROM AUTHOR]