2D Yang-Mills Theory Research Articles

Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism.

Magnetic excitations play a crucial role in understanding the color confinement of 4D Yang-Mills theory, and we have the monopole and the center vortex as plausible candidates to explain its mechanism. Under suitable compactified setups of 4D Yang-Mills theory, we can achieve different weakly coupled descriptions of confinement phenomena: The monopole mechanism takes place on R^{3}×S^{1} with the double-trace deformation, and the center-vortex mechanism is effective on R^{2}×T^{2} with the 't Hooft flux. We unify these two semiclassical descriptions by showing the explicit relation between the monopole and center vortex.

Dimensional reduction gauge and effective dimensional reduction in four-dimensional Yang-Mills theory

Motivated by one-dimensional color-electric flux-tube formation in four-dimensional (4D) QCD, we investigate a possibility of effective dimensional reduction in the 4D Yang-Mills (YM) theory. We propose a new gauge fixing of “dimensional reduction (DR) gauge” defined so as to minimize RDR≡∫d4sTr[Ax2(s)+Ay2(s)], which has a residual gauge symmetry for the gauge function Ω(t,z) like 2D QCD on the t−z plane. We investigate effective dimensional reduction in the DR gauge using SU(3) quenched lattice QCD at β=6.0. The amplitude of Ax(s) and Ay(s) are found to be strongly suppressed in the DR gauge. We consider “tz-projection” of Ax,y(s)→0 for the gauge configuration generated in the DR gauge, in a similar sense to Abelian projection in the maximally Abelian gauge. By the tz-projection in the DR gauge, the interquark potential is not changed, and At(s) and Az(s) play a dominant role in quark confinement. In the DR gauge, we calculate a spatial correlation ⟨TrA⊥(s)A⊥(s+ra⊥)⟩(⊥=x,y) and estimate the spatial mass of A⊥(s)(⊥=x,y) as M≃1.7 GeV. It is conjectured that this large mass makes A⊥(s) inactive and realizes the dominance of At(s) and Az(s) in infrared region in the DR gauge. We also calculate the spatial correlation of two temporal link-variables and find that the correlation decreases as exp(−mr) with m≃0.6 GeV. Using a crude approximation, the 4D YM theory is reduced into an ensemble of 2D YM systems with the coupling of g2D=gm. Published by the American Physical Society 2024

Simulating dimensionally reduced 4D Yang-Mills theory on a quantum computer

Simulating dimensionally reduced 4D Yang-Mills theory on a quantum computer

Quadratic Twist-Noncommutative Gauge Theory.

Studies of noncommutative gauge theory have mainly focused on noncommutative spacetimes with constant noncommutative structure, with little known about actions for noncommutative 4D Yang-Mills theory beyond this case. We construct an action for Yang-Mills theory on a quadratically noncommutative spacetime, i.e., of quantum-plane type, obtained from a Drinfeld twist, with star-gauge symmetry. Applied to supersymmetric Yang-Mills theory, this gives a candidate AdS/CFT dual of string theory on a related deformation of AdS_{5}×S^{5}, which is expected to be integrable in the planar limit.

Structure of Kaluza-Klein graviton scattering amplitudes from the gravitational equivalence theorem and double copy

We study the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the gravitational KK Goldstone bosons in the compactified 5d General Relativity (GR). We analyze the geometric "Higgs" mechanism for mass-generation of KK gravitons under compactification with a general $R_\xi$ gauge-fixing, which is free from the vDVZ discontinuity. Then, we formulate the Gravitational Equivalence Theorem (GRET) to connect the longitudinal KK graviton amplitudes to the KK Goldstone amplitudes, which is a manifestation of the geometric Higgs mechanism at $S$-matrix level. We directly compute the tree-level KK Goldstone amplitudes which equal the longitudinal KK graviton amplitudes in the high energy limit. We further extend the double-copy method with color-kinematics duality to reconstruct the massive KK longitudinal graviton (Goldstone) amplitudes from the KK longitudinal gauge boson (Goldstone) amplitudes in the compactified 5d Yang-Mills (YM) theory under high energy expansion. From these, we reconstruct the GRET of the KK longitudinal graviton (Goldstone) amplitudes in the 5d GR from the KK longitudinal gauge boson (Goldstone) amplitudes in the 5d YM theory. Using either the GRET or the double-copy reconstruction, we provide a theoretical mechanism showing that the sum of all the energy-power terms [up to $O(E^{10})$] in the high-energy four longitudinal KK graviton amplitudes must cancel down to $O(E^2)$ as enforced by matching the energy-power dependence of the corresponding KK Goldstone amplitudes or by matching that of the double-copy amplitudes from the KK YM theory. With the double-copy approach, we establish a new correspondence between the two energy-cancellations: $E^4 \to E^0$ in the 5d KK YM theory and $E^{10} \to E^2$ in the 5d KK GR theory. We further analyze the structure of the residual terms in the GRET and uncover a new energy-cancellation mechanism therein.

Generalizations of the double-copy: the KLT bootstrap

We formulate a new program to generalize the double-copy of tree amplitudes. The approach exploits the link between the identity element of the “KLT algebra” and the KLT kernel, and we demonstrate how this leads to a set of KLT bootstrap equations that the double-copy kernel has to satisfy in addition to locality constraints. We solve the KLT bootstrap equations perturbatively to find the most general higher-derivative corrections to the 4- and 5-point field theory KLT kernel. The new kernel generalizes the string KLT kernel and its associated monodromy relations. It admits new color-structures in the effective theories it double-copies. It provides distinct generalized KK and BCJ relations for the left and right single-color theories and is in that sense a ‘heterotic’-type double-copy. We illustrate the generalized double-copy in detail for 4d Yang-Mills theory with higher-derivative corrections that produce dilaton-axion-gravity with local operators up order ∇10R4. Finally, we initiate a search for new double-copy kernels.

From 2d droplets to 2d Yang-Mills

We establish a connection between time evolution of free Fermi droplets and partition function of generalised q-deformed Yang-Mills theories on Riemann surfaces. Classical phases of (0+1) dimensional unitary matrix models can be characterised by free Fermi droplets in two dimensions. We quantise these droplets and find that the modes satisfy an abelian Kac-Moody algebra. The Hilbert spaces H+ and H− associated with the upper and lower free Fermi surfaces of a droplet admit a Young diagram basis in which the phase space Hamiltonian is diagonal with eigenvalue, in the large N limit, equal to the quadratic Casimir of u(N). We establish an exact mapping between states in H± and geometries of droplets. In particular, coherent states in H± correspond to classical deformation of upper and lower Fermi surfaces. We prove that correlation between two coherent states in H± is equal to the chiral and anti-chiral partition function of 2d Yang-Mills theory on a cylinder. Using the fact that the full Hilbert space H+⊗H− admits a composite basis, we show that correlation between two classical droplet geometries is equal to the full U(N) Yang-Mills partition function on cylinder. We further establish a connection between higher point correlators in H± and higher point correlators in 2d Yang-Mills on Riemann surface. There are special states in H± whose transition amplitudes are equal to the partition function of 2d q-deformed Yang-Mills and in general character expansion of Villain action. We emphasise that the q-deformation in the Yang-Mills side is related to special deformation of droplet geometries without deforming the gauge group associated with the matrix model.

Dual Superconductor Model of Confinement: Quantum-String Representation of the 4D Yang–Mills Theory on a Torus and the Correlation Length away from the London Limit

This paper is devoted to the dual superconductor model of confinement in the 4D Yang–Mills theory. In the first part, we consider the latter theory compactified on a torus, and use the dual superconductor model in order to obtain the Polchinski–Strominger term in the string representation of a Wilson loop. For a certain realistic critical value of the product of circumferences of the compactification circles, which is expressed in terms of the gluon condensate and the vacuum correlation length, the coupling of the Polchinski–Strominger term turns out to be such that the string conformal anomaly cancels out, making the string representation fully quantum. In the second part, we use the analogy between the London limit of the dual superconductor and the low-energy limit of the 4D compact QED, to obtain the partition function of the dual superconductor model away from the London limit. There, we find a decrease of the vacuum correlation length, and derive the corresponding potential of monopole currents.

Kaluza-Klein from colour-kinematics duality for massive fields

We consider a broad class of massive four dimensional effective theories describing an infinite tower of charged massive spin 1 states, interacting with massless spin 1 and spin 0. The spectrum is chosen to be the same as that appears in the Kaluza-Klein theory reduction of 5d Yang-Mills to ensure the absence of any spurious poles in a possible double copy formulation. The effective theories are characterized by multiple different couplings between different fields which are unconstrained by symmetries and low energy criteria. Remarkably, by demanding that the scattering amplitudes preserve colour-kinematics duality for different scattering processes, required for the existence of a massive double copy, we find that our 4d Lagrangian is fixed uniquely to the Kaluza-Klein compactification of 5d Yang-Mills theory together with its known double copy consistent higher derivative operators.

Boson-fermion correspondence and holomorphic anomaly equation in 2d Yang-Mills theory on torus

Recently, Okuyama and Sakai proposed a novel holomorphic anomaly equation for the partition function of 2d Yang-Mills theory on a torus, based on an anholomorphic deformation of the propagator in the bosonic formulation. Using the boson-fermion correspondence, we derive the formula for the deformed partition function in fermionic description and give a proof of the holomorphic anomaly equation.

Schur correlation functions from q -deformed Yang-Mills theory

We construct the wave functions in the $q$-deformed 2D Yang-Mills theory that compute torus correlation functions of affine currents in the vertex operator algebra associated to a class of 4D $\mathcal{N}=2$ superconformal field theory. These wave functions are then shown to reduce to the topological correlators of a set of Coulomb branch operators in the $T[SU(N)]$ theory, from which those correlators in the 3D mirror dual of the 4D ${T}_{N}$ theories can be computed.

Semiclassical limit of topological R\xe9nyi entropy in 3d Chern-Simons theory

We study the multi-boundary entanglement structure of the state associated with the torus link complement S3\\Tp,q in the set-up of three-dimensional SU(2)k Chern-Simons theory. The focal point of this work is the asymptotic behavior of the Rényi entropies, including the entanglement entropy, in the semiclassical limit of k → ∞. We present a detailed analysis of several torus links and observe that the entropies converge to a finite value in the semiclassical limit. We further propose that the large k limiting value of the Rényi entropy of torus links of type Tp,pn is the sum of two parts: (i) the universal part which is independent of n, and (ii) the non-universal or the linking part which explicitly depends on the linking number n. Using the analytic techniques, we show that the universal part comprises of Riemann zeta functions and can be written in terms of the partition functions of two-dimensional topological Yang-Mills theory. More precisely, it is equal to the Rényi entropy of certain states prepared in topological 2d Yang-Mills theory with SU(2) gauge group. Further, the universal parts appearing in the large k limits of the entanglement entropy and the minimum Rényi entropy for torus links Tp,pn can be interpreted in terms of the volume of the moduli space of flat connections on certain Riemann surfaces. We also analyze the Rényi entropies of Tp,pn link in the double scaling limit of k → ∞ and n → ∞ and propose that the entropies converge in the double limit as well.

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.

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.

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.