2D Yang-Mills Research Articles

On a gravity dual to flavored topological quantum mechanics

In this paper, we propose a generalization of the AdS2/CFT1 correspondence constructed by Mezei, Pufu and Wang in [1], which is the duality between 2d Yang-Mills theory with higher derivatives in the AdS2 background, and 1d topological quantum mechanics of two adjoint and two fundamental U(N ) fields, governing certain protected sector of operators in 3d ABJM theory at the Chern-Simons level k = 1. We construct a holographic dual to a flavored generalization of the 1d quantum mechanics considered in [1], which arises as the effective field theory living on the intersection of stacks of N D2-branes and k D6-branes in the Ω-background in Type IIA string theory, and describes the dynamics of the protected sector of operators in mathcal{N} = 4 theory with k fundamental hypermultiplets, having a holographic description as M-theory in the AdS4× S7/ℤk background. We compute the structure constants of the bulk theory gauge group, and construct a map between the observables of the boundary theory and the fields of the bulk theory.

Topological sectors for heterotic M5-brane charges under Hypothesis H

Assuming Fiorenza-Sati-Schreiber’s Hypothesis H, on the charge quantization of M-theory’s C -field, the topological sectors of the resulting Stringc2 (4)-valued higher gauge theory on a heterotic M5-brane are classified by homotopy classes of maps from the worldvolume ΣM5 to BStringc2 (4). This note calculates the sectors in a number of examples of M5-brane topology, including examples considered in the 3d-3d correspondence, the emergence of skyrmions from higher-dimensional instantons and Witten’s analysis of the S-duality of 4d Yang-Mills theory.

Spontaneous symmetry breaking in pure 2D Yang-Mills theory

We consider purely topological 2D Yang-Mills theory on a torus with the second Stiefel-Whitney class added to the Lagrangian in the form of a $\ensuremath{\theta}$ term. It will be shown that at $\ensuremath{\theta}=\ensuremath{\pi}$ there exists a class of $SU(2N)/{\mathbb{Z}}_{2}$ ($N>1$) gauge theories with a twofold degenerate vacuum, which spontaneously breaks the time reversal and charge conjugation symmetries. The corresponding order parameter is given by the generator $\mathcal{O}$ of the ${\mathbb{Z}}_{N}$ one-form symmetry.

Fully Quantum String Representation of a Wilson Loop in the Finite-Temperature 3D Yang–Mills Theory

We demonstrate the emergence of the Polchinski–Strominger term in the string representation of a Wilson loop in the confinement phase of the finite-temperature 3D Yang–Mills theory. At a temperature which is roughly twice smaller than the deconfinement critical temperature, the value of the coupling of that term becomes such that the string conformal anomaly cancels out, thereby admitting a fully quantum description of the quark–antiquark string in 3D rather than 26D.

Isolated Singularities of Yang–Mills–Higgs Fields on Surfaces

Abstract We study isolated singularities of 2D Yang–Mills–Higgs (YMH) fields defined on a fiber bundle, where the fiber space is a compact Riemannian manifold and the structure group is a compact connected Lie group. In general, the singularity cannot be removed due to possibly non-vanishing limit holonomy around the singular points. We establish a sharp asymptotic decay estimate of the YMH field near a singular point, where the decay rate is precisely determined by the limit holonomy. Our result can be viewed as a generalization of the classical removable singularity theorem of 2D harmonic maps.

3D Yang-Mills confining properties from a non-Abelian ensemble perspective

In this work, we propose a 3D ensemble measure for center-vortex worldlines and chains equipped with non-Abelian degrees of freedom. We derive an effective field description for the center-element average where the vortices get represented by N flavors of effective Higgs fields transforming in the fundamental representation. This field content is required to accommodate fusion rules where N vortices can be created out of the vacuum. The inclusion of the chain sector, formed by center-vortex worldlines attached to pointlike defects, leads to a discrete set of Z(N) vacua. This type of SSB pattern supports the formation of a stable domain wall between quarks, thus accommodating not only a linear potential but also the Luscher term. Moreover, after a detailed analysis of the associated field equations, the asymptotic string tension turns out to scale with the quadratic Casimir of the antisymmetric quark representation. These behaviors reproduce those derived from Monte Carlo simulations in SU(N) 3D Yang-Mills theory, which lacked understanding in the framework of confinement as due to percolating magnetic defects.

Two faces of Douglas-Kazakov transition: From Yang-Mills theory to random walks and beyond

Being inspired by the connection between 2D Yang-Mills (YM) theory and (1+1)D “vicious walks” (VW), we consider different incarnations of large-N Douglas-Kazakov (DK) phase transition in gauge field theories and stochastic processes focusing at possible physical interpretations. We generalize the connection between YM and VW, study the influence of initial and final distributions of walkers on the DK phase transition, and describe the effect of the θ-term in corresponding stochastic processes. We consider the Jack stochastic process involving Calogero-type interaction between walkers and investigate the dependence of DK transition point on a coupling constant. Relying on the relation between large-N 2D q-YM and extremal black hole (BH) with large-N magnetic charge, we speculate about a physical interpretation of a DK phase transitions in a 4D extremal charged BH.

Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory

We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at $\theta=\pi$ (SU(2)$_{\theta=\pi}$ YM), by turning on background fields for both the time-reversal (i.e., on unorientable manifolds) and 1-form center global symmetry. We find four classes of time-reversal and Lorentz symmetry-enriched SU(2)$_{\theta=\pi}$ YM, labeled by $(K_1, K_2)$: $K_1=0,1$ specifies Kramers singlet/doublet Wilson line and new mixed higher 't Hooft anomalies; $K_2=0,1$ specifies boson/fermionic Wilson line and a new Wess-Zumino-Witten-like counterterm. Higher anomalies indicate that to realize all higher $n$-global symmetries locally on $n$-simplices, the 4d theory becomes a boundary of a 5d higher-symmetry-protected topological state (SPTs, as an invertible topological quantum field theory (TQFT) or a cobordism invariant in math, or as a 5d higher-symmetric interacting topological superconductor in condensed matter). By dynamically gauging the 1-form symmetry, we transform a 5d bulk SRE SPTs into an LRE symmetry-enriched topologically ordered state (SETs); thus we obtain the 4d SO(3)$_{\theta=\pi}$ YM-5d LRE-higher-SETs coupled system with higher-form gauge fields. We further derive new exotic anyonic statistics of extended objects such as 2-worldsheet of strings and 3-worldvolume of branes, physically characterizing the 5d SETs. We discover triple and quadruple link invariants associated with the 5d higher-gauge TQFTs, hinting at a relation between non-supersymmetric 4d pure YM and topological links in 5d. We provide 4d-5d lattice simplicial complex regularizations and bridge to 4d quantum spin liquids. We constrain gauge dynamics by higher anomalies and a higher symmetry-extension method.

One-loop \u03b2-functions in 4-derivative gauge theory in 6 dimensions

A classically scale-invariant 6d analog of the 4d Yang-Mills theory is the 4-derivative (∇F )2 + F 3 gauge theory with two independent couplings. Motivated by a search for a perturbatively conformal but possibly non-unitary 6d models we compute the one-loop β-functions in this theory. A systematic way of doing this using the back-ground field method requires the (previously unknown) expression for the b6 Seeley-DeWitt coefficient for a generic 4-derivative operator; we derive it here. As an application, we also compute the one-loop β-function in the (1,0) supersymmetric (∇F )2 6d gauge theory con-structed in hep-th/0505082.

Holomorphic anomaly of 2d Yang-Mills theory on a torus revisited

We study the large N ’t Hooft expansion of the chiral partition function of 2d U(N) Yang-Mills theory on a torus. There is a long-standing puzzle that no explicit holomorphic anomaly equation is known for the partition function, although it admits a topological string interpretation. Based on the chiral boson interpretation we clarify how holomorphic anomaly arises and propose a natural anti-holomorphic deformation of the partition function. Our deformed partition function obeys a fairly traditional holomorphic anomaly equation. Moreover, we find a closed analytic expression for the deformed partition function. We also study the behavior of the deformed partition function both in the strong coupling/large area limit and in the weak coupling/small area limit. In particular, we observe that drastic simplification occurs in the weak coupling/small area limit, giving another nontrivial support for our anti-holomorphic deformation.

Skyrme and Faddeev models in the low-energy limit of 4d Yang–Mills–Higgs theories

Firstly, we consider U(Nc) Yang–Mills gauge theory on R3,1 with Nf>Nc flavours of scalar fields in the fundamental representation of U(Nc). The moduli space of vacua is the Grassmannian manifold Gr(Nc,Nf). It is shown that for strong gauge coupling this 4d Yang–Mills–Higgs theory reduces to the Faddeev sigma model on R3,1 with Gr(Nc,Nf) as target. Its action contains the standard two-derivative sigma-model term as well as the four-derivative Skyrme-type term, which stabilizes solutions against scaling. Secondly, we consider a Yang–Mills–Higgs model with Nf=2Nc and a Higgs potential breaking the flavour group U(Nf)=U(2Nc) to U+(Nc)×U−(Nc), realizing the simplest A2⊕A2-type quiver gauge theory. The vacuum moduli space of this model is the group manifold Uh(Nc) which is the quotient of U+(Nc)×U−(Nc) by its diagonal subgroup. When the gauge coupling constant is large, this 4d Yang–Mills–Higgs model reduces to the Skyrme sigma model on R3,1 with Uh(Nc) as target. Thus, both the Skyrme and the Faddeev model arise as effective field theories in the infrared of Yang–Mills–Higgs models.

Calculating non-perturbative quantities through the world-line formalism

We present two applications of the world-line formalism to the calculation of non-perturbative quantities in QCD. The first quantity is the free energy of the gluon plasma in the high-temperature limit; the second quantity is the pair-production rate in the chromo-electric field of a flux tube. In the first case, where effects of spatial confinement in the dimensionally-reduced 3D Yang-Mills theory are primarily important, we calculate the free-energy density of a gluon propagating in the stochastic background fields through a suitable parametrization of the area-and the perimeter laws of the Wilson loop, which enters the corresponding one-loop effective action. In this way, we find that the order of the leading correction to the Stefan-Boltzmann free energy changes from for N ∼ 1 to for N ≫ 1, where λ is the finite-temperature’t Hooft coupling, and N is the number of colors. In the second case, we find that, in the London limit of the dual superconductor, the Schwinger pair-production rate, ∼ e−const·m2, goes over to e−const·m. Given that the flux-tube field is static, we find such a conversion of the Gaussian distribution into an exponential one, remarkable.

Large N phase transition in Toverline{T} -deformed 2d Yang-Mills theory on the sphere

We study the partition function of a Toverline{T} -deformed version of Yang-Mills theory on the two-sphere. We show that the Douglas-Kazakov phase transition persists for a range of values of the deformation parameter, and that the critical area is lowered. The transition is of third order and also induced by instantons, whose contributions we characterize.

Chaos from equivariant fields on fuzzy S4

We examine the 5d Yang-Mills matrix model in 0 + 1-dimensions with U(4N) gauge symmetry and a mass deformation term. We determine the explicit SU(4) ≈ SO(6) equivariant parametrizations of the gauge field and the fluctuations about the classical four concentric fuzzy four sphere configuration and obtain the low energy reduced actions(LEAs) by tracing over the SF4s for the first five lowest matrix levels. The LEAs so obtained have potentials bounded from below indicating that the equivariant fluctuations about the SF4 do not lead to any instabilities. These reduced systems exhibit chaos, which we reveal by computing their Lyapunov exponents. Using our numerical results, we explore various aspects of chaotic dynamics emerging from the LEAs. In particular, we model how the largest Lyapunov exponents change as a function of the energy. We also show that, in the Euclidean signature, the LEAs support the usual kink type soliton solutions, i.e. instantons in 1+ 0-dimensions, which may be seen as the imprints of the topological fluxes penetrating the concentric SF4s due to the equivariance conditions, and preventing them to shrink to zero radius. Relaxing the Gauss law constraint in the LEAs in the manner recently discussed by Maldacena and Milekhin leads to Goldstone bosons.

Edge dynamics from the path integral \u2014 Maxwell and Yang-Mills

We derive an action describing edge dynamics on interfaces for gauge theories (Maxwell and Yang-Mills) using the path integral. The canonical structure of the edge theory is deduced and the thermal partition function calculated. We test the edge action in several applications. For Maxwell in Rindler space, we recover earlier results, now embedded in a dynamical canonical framework. A second application is 2d Yang-Mills theory where the edge action becomes just the particle-on-a-group action. Correlators of boundary-anchored Wilson lines in 2d Yang-Mills are matched with, and identified as correlators of bilocal operators in the particle-on-a-group edge model.

Generalised Born-Infeld models, Lax operators and the mathrm{T}overline{mathrm{T}} perturbation

Surprising links between the deformation of 2D quantum field theories induced by the composite mathrm{T}overline{mathrm{T}} operator, effective string models and the AdS/CFT correspondence, have recently emerged. The purpose of this article is to discuss various classical aspects related to the deformation of 2D interacting field theories. Special attention is given to the sin(h)-Gordon model, for which we were able to construct the mathrm{T}overline{mathrm{T}} -deformed Lax pair. We consider the Lax pair formulation to be the first essential step toward a more satisfactory geometrical interpretation of this deformation within the integrable model framework.Furthermore, it is shown that the 4D Maxwell-Born-Infeld theory, possibly with the addition of a mass term or a derivative-independent potential, corresponds to a natural extension of the 2D examples. Finally, we briefly comment on 2D Yang-Mills theory and propose a modification of the heat kernel, for a generic surface with genus p and n boundaries, which fully accounts for the mathrm{T}overline{mathrm{T}} contribution.

Resurgence analysis of 2d Yang-Mills theory on a torus

We study the large N ’t Hooft expansion of the partition function of 2d U(N) Yang-Mills theory on a torus. We compute the 1/N genus expansion of both the chiral and the full partition function of 2d Yang-Mills using the recursion relation found by Kaneko and Zagier with a slight modification. Then we study the large order behavior of this genus expansion, from which we extract the non-perturbative correction using the resurgence relation. It turns out that the genus expansion is not Borel summable and the coefficient of 1-instanton correction, the so-called Stokes parameter, is pure imaginary. We find that the non-perturbative correction obtained from the resurgence is reproduced from a certain analytic continuation of the grand partition function of a system of non-relativistic fermions on a circle. Our analytic continuation is different from that considered in hep-th/0504221.

Topology in the 2d Heisenberg Model under Gradient Flow

The 2d Heisenberg model — or 2d O(3) model — is popular in condensed matter physics, and in particle physics as a toy model for QCD. Along with other analogies, it shares with 4d Yang-Mills theories, and with QCD, the property that the configurations are divided in topological sectors. In the lattice regularisation the topological charge Q can still be defined such that . It has generally been observed, however, that the topological susceptibility does not scale properly in the continuum limit, i.e. that the quantity diverges for ξ → ∞ (where ξ is the correlation length in lattice units). Here we address the question whether or not this divergence persists after the application of the Gradient Flow.

Half-BPS Wilson loop and AdS2/CFT1

We study correlation functions of local operator insertions on the 1/2-BPS Wilson line in N=4 super Yang–Mills theory. These correlation functions are constrained by the 1d superconformal symmetry preserved by the 1/2-BPS Wilson line and define a defect CFT1 living on the line. At strong coupling, a set of elementary operator insertions with protected scaling dimensions correspond to fluctuations of the dual fundamental string in AdS×5S5 ending on the line at the boundary and can be thought of as light fields propagating on the AdS2 worldsheet. We use AdS/CFT techniques to compute the tree-level AdS2 Witten diagrams describing the strong coupling limit of the four-point functions of the dual operator insertions. Using the OPE, we also extract the leading strong coupling corrections to the anomalous dimensions of the “two-particle” operators built out of elementary excitations. In the case of the circular Wilson loop, we match our results for the 4-point functions of a special type of scalar insertions to the prediction of localization to 2d Yang–Mills theory.

From 4d Yang-Mills to 2d \u2102\u2119N\u2009\u2212\u20091 model: IR problem and confinement at weak coupling

We study four-dimensional SU(N) Yang-Mills theory on mathbb{R}times {mathbb{T}}^3=mathbb{R}times {S}_A^1times {S}_B^1times {S}_C^1 , with a twisted boundary condition by a ℤN center symmetry imposed on SB1 × SC1. 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 {mathbb{T}}^2={S}_Atimes {S}_B , to connect the model to the two-dimensional ℂℙN− 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 ℤN global symmetry of ℂℙN− 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.