3d SU Research Articles

Symmetries, universes and phases of QCD2 with an adjoint Dirac fermion

We study 2d SU(N) QCD with an adjoint Dirac fermion. Assuming that the IR limit of the massless theory is captured by a WZW coset CFT, we show that this CFT can be decomposed into a sum of distinct CFTs, each representing a superselection sector (universe) of the gauge theory corresponding to different flux tube sectors. The CFTs describing each universe are related by non-invertible topological lines that exhibit a mixed anomaly with the ℤN1 1-form symmetry. These symmetries exists along the entire RG flow thereby implying deconfinement of the massless theory. We begin by outlining the general features of the model for arbitrary N and then provide a detailed analysis for N = 2 and N = 3. In these specific cases, we explicitly determine the IR partition function, identify the symmetries, and explore relevant deformations. Based on these findings and in alignment with various previous studies, we propose a phase diagram for the massive SU(2) gauge theory and calculate its confining string tension.

A new solution to the Callan Rubakov effect

In this paper we study the scattering of massive fermions off of smooth, spherically symmetric monopoles in 4d SU(2) gauge theory. We propose a complete physical picture of the monopole-fermion interaction which encompasses all angular momentum modes. We show that as an in-going fermion scatters off a monopole, it excites trapped W-bosons in the monopole core by a version of the Witten effect so that the monopole can accrue charge and transform into a dyon at parametrically low energies. The imparted electric charge is then protected from decay by an emergent ℤN generalized global symmetry, creating a stable dyon. At sufficiently low energies, the scattered fermion can be trapped by the dyon’s electrostatic potential, forming a bound state, which can decay into spherically symmetric fermion modes subject to the preserved ℤN global symmetry. We propose that monopole-fermion scattering can be described in this way without needing to add “new” states to the Hilbert space, thereby eliminating a long standing confusion in the Callan Rubakov effect.

Charged critical behavior and nonperturbative continuum limit of three-dimensional lattice SU(Nc) gauge Higgs models

We consider three-dimensional (3D) lattice SU(Nc) gauge Higgs theories with multicomponent (Nf>1) degenerate scalar fields and U(Nf) global symmetry, focusing on systems with Nc=2, to identify critical behaviors that can be effectively described by the corresponding 3D SU(Nc) gauge Higgs field theory. The field-theoretical analysis of the RG flow allows one to identify a stable charged fixed point for large values of Nf, that would control transitions characterized by the global symmetry-breaking pattern U(Nf)→SU(2)⊗U(Nf−2). Continuous transitions with the same symmetry-breaking pattern are observed in the SU(2) lattice gauge model for Nf≥30. Here we present a detailed finite-size scaling analysis of the Monte Carlo data for several large values of Nf. The results are in substantial agreement with the field-theoretical predictions obtained in the large-Nf limit. This provides evidence that the SU(Nc) gauge Higgs field theories provide the correct effective description of the 3D large-Nf continuous transitions between the disordered and the Higgs phase, where the flavor symmetry breaks to SU(2)⊗U(Nf−2). Therefore, at least for large enough Nf, the 3D SU(Nc) gauge Higgs field theories with multicomponent scalar fields can be nonperturbatively defined by the continuum limit of lattice discretized models with the same local and global symmetries. Published by the American Physical Society 2024

Combinatorial summation of Feynman diagrams

Feynman’s diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a universal framework for efficient summation of connected or skeleton Feynman diagrams for generic quantum many-body systems. It is based on an explicit combinatorial construction of the sum of the integrands by dynamic programming, at a computational cost that can be made only exponential in the diagram order on a classical computer and potentially polynomial on a quantum computer. We illustrate the technique by an unbiased diagrammatic Monte Carlo calculation of the equation of state of the 2D SU(N) Hubbard model in an experimentally relevant regime, which has remained challenging for state-of-the-art numerical methods.

Full QCD with milder topological freezing

We simulate Nf = 2 + 1 QCD at the physical point combining open and periodic boundary conditions in a parallel tempering framework, following the original proposal by M. Hasenbusch for 2d CPN−1 models, which has been recently implemented and widely employed in 4d SU(N) pure Yang-Mills theories too. We show that using this algorithm it is possible to achieve a sizable reduction of the auto-correlation time of the topological charge in dynamical fermions simulations both at zero and finite temperature, allowing to avoid topology freezing down to lattice spacings as fine as a ∼ 0.02 fm. Therefore, this implementation of the Parallel Tempering on Boundary Conditions algorithm has the potential to substantially push forward the investigation of the QCD vacuum properties by means of lattice simulations.

Wilson loops and random matrices

Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories.

Non-supersymmetric duality cascade of QCD(BF) via semiclassics on ℝ2× T2 with the baryon-’t Hooft flux

We study the phase diagrams of the bifundamental QCD (QCD(BF)) of different ranks, which is the 4d SU(N1) × SU(N2) gauge theory coupled with a bifundamental Dirac fermion. After discussing the anomaly constraints on possible vacuum structures, we apply a novel semiclassical approach on ℝ2× T2 with the baryon-’t Hooft flux to obtain the concrete dynamics. The 2d effective theory is derived by the dilute gas approximation of center vortices, and it serves as the basis for determining the phase diagram of the model under the assumption of adiabatic continuity. As an application, we justify the non-supersymmetric duality cascade between different QCD(BF), which has been conjectured in the large-N argument. Combined with the semiclassics and the large-N1,2 limit, we construct the explicit duality map from the parent theory, SU(N1) × SU(N2) QCD(BF), to the daughter theory, SU(N1) × SU(N2− N1) QCD(BF), including the correspondence of the coupling constants. We numerically examine the validity of the duality also for finite N1,2 within our semiclassics, finding a remarkable agreement of the phase diagrams between the parent and daughter sides.

Localization and resummation of unstable instantons in 2d Yang-Mills

We compute the exact all-orders perturbative expansion for the partition function of 2d SU(2) Yang-Mills theory on closed surfaces around higher critical points of the classical action. We demonstrate that the expansion can be derived from the lattice partition function for all genera using a distributional generalization of the Poisson summation formula. We then recompute the expansion directly, using a stationary phase version of supersymmetric localization. The result of localization is a novel effective action which is itself a distribution rather than a function of the supersymmetric moduli. We comment on possible applications to A-twisted models and their analogs in higher dimensions.

Sporadic dualities from tensor deconfinement

In this paper we give a field theory explanation of two confining dualities that have been proposed in the literature based on exact results from supersymmetric localization. The first confining model under investigation is 4d SU(Nc + 1) SQCD with a conjugate rank-2 anti-symmetric tensor, Nc + 3 anti-fundamentals, 2Nc fundamentals and a superpotential that couples the anti-symmetric tensor and the fundamentals. The second confining model studied here is 3dN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 USp(4) gauge SQCD with two fundamentals, two rank-2 anti-symmetric tensors and vanishing superpotential. Here we prove that these models are confining by using the technique of deconfining the anti-symmetric tensors and then by flowing to the IR description by sequential dualities. As a bonus the analysis provides (alternative) proofs of the identities obtained from supersymmetric localization.

Equation of State and Thermometry of the 2D SU(N) Fermi-Hubbard Model.

We characterize the equation of state (EoS) of the SU(N>2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N=3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum MonteCarlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.

The dynamics of zero modes in lattice gauge theory — difference between SU(2) and SU(3) in 4D

The dynamics of zero modes in gauge theory is highly nontrivial due to its nonperturbative nature even in the case where the other modes can be treated perturbatively. One of the related issues concerns the possible instability of the trivial vacuum Aμ(x) = 0 due to the existence of nontrivial degenerate vacua known as “torons”. Here we investigate this issue for the 4D SU(2) and SU(3) pure Yang-Mills theories on the lattice by explicit Monte Carlo calculation of the Wilson loops and the Polyakov line at large β. While we confirm the leading 1/β predictions obtained around the trivial vacuum in both SU(2) and SU(3) cases, we find that the subleading term vanishes only logarithmically in the SU(2) case unlike the power-law decay in the SU(3) case. In fact, the 4D SU(2) case is marginal according to the criterion by Coste et al. Here we show that the trivial vacuum dominates in this case due to large fluctuations of the zero modes around it, thereby providing a clear understanding of the observed behaviors.

Fermions with SU(1, n) spacetime symmetry

We construct theories of free fermions in (2n − 1)-dimensions with SU(1, n) spacetime symmetry from the null reduction of fermions on a 2n-dimensional Ω-deformed Minkowski background for n = 2 and n = 3. These play a role in the 5d SU(1, 3)-invariant theories that are conjectured to offer a full description of certain 6d superconformal field theories. We find the (2n − 1)-dimensional manifestation of the supersymmetry of a free 2n-dimensional boson-fermion system, which we use to fix the fermion two-point functions. It is then shown that the full 2n-dimensional two-point function can be recovered through resummation. Limits of the theories are considered, and it is observed that both Galilean and Carrollian field theories appear in different regimes. We confirm that the correlation functions obey the SU(1, n) Ward identities and the representations of the fermions under this group are discussed.

Topology of SU(N) lattice gauge theories coupled with ℤN 2-form gauge fields

We extend the definition of Lüscher’s lattice topological charge to the case of 4d SU(N) gauge fields coupled with ℤN 2-form gauge fields. This result is achieved while maintaining the locality, the SU(N) gauge invariance, and ℤN 1-form gauge invariance, and we find that the manifest 1-form gauge invariance plays the central role in our construction. This result gives the lattice regularized derivation of the mixed ’t Hooft anomaly in pure SU(N) Yang-Mills theory between its ℤN 1-form symmetry and the θ periodicity.

Construction of irregular conformal/W block and flavor mass relations of [formula omitted] SUSY gauge theory from the An−1 quiver matrix model

A sequence of massive scaling limits of the β-deformed An−1 quiver matrix model that keeps the size of the matrices finite and that corresponds to the Nf=2n→2n−1,2n−2 limits on the number of flavors at 4d su(n)N=2 SUSY gauge theory side is carried out to provide us with the integral representation of su(n) irregular conformal/W block. The original paths are naturally deformed into those in the complex plane, permitting us to convert into an su(n) extension of the unitary matrix model of GWW type with a set of log potentials for all species of eigenvalues. Looking at the region in the parameter space that enjoys the maximal symmetry of the model, we derive a set of relations among the mass parameters which may serve as evidence for the existence of the Argyres-Douglas critical hypersurface.

One-loop algebras and fixed flow trajectories in adjoint multi-scalar gauge theory

We study the one loop renormalisation of 4d SU(N) Yang-Mills theory with M adjoint representation scalar multiplets related by O(M) symmetry. General M are of field theoretic interest, and the 4d one loop beta function of the gauge coupling g2 vanishes for the case M = 22, which is intriguing for string theory. This case is related to D3 branes of critical bosonic string theory in D = 22 + 4 = 26. An RG fixed point could have provided a definition for a purely bosonic AdS/CFT, but we show that scalar self-couplings λ ruin one-loop conformal invariance in the large N limit. There are real fixed flows (fixed points of λ/g2) only for M ≥ 406, rendering one-loop fixed points of the gauge coupling and scalar couplings incompatible.We develop and check an algebraic approach to the one-loop renormalisation group which we find to be characterised by a non-associative algebra of marginal couplings. In the large N limit, the resulting RG flows typically suffer from strong coupling in both the ultraviolet and the infrared. Only for M ≥ 406 fine-tuned solutions exist which are weakly coupled in the infrared.

Free energy on the sphere for non-abelian gauge theories

We compute the Sd partition function of the fixed point of non-abelian gauge theories in continuous d, using the ϵ-expansion around d = 4. We illustrate in detail the technical aspects of the calculation, including all the factors arising from the gauge-fixing procedure, and the method to deal with the zero-modes of the ghosts. We obtain the result up to NLO, i.e. including two-loop vacuum diagrams. Depending on the sign of the one-loop beta function, there is a fixed point with real gauge coupling in d > 4 or d < 4. In the first case we extrapolate to d = 5 to test a recently proposed construction of the UV fixed point of 5d SU(2) Yang-Mills via a susy-breaking deformation of the E1 SCFT. We find that the F theorem allows the proposed RG flow. In the second case we extrapolate to d = 3 to test whether QCD3 with gauge group SU(nc) and nf fundamental matter fields flows to a CFT or to a symmetry-breaking case. We find that within the regime with a real gauge coupling near d = 4 the CFT phase is always favored. For lower values of nf we compare the average of F between the two complex fixed points with its value at the symmetry-breaking phase to give an upper bound of the critical value {n}_f^{ast } below which the symmetry-breaking phase takes over.

On the 4d superconformal index near roots of unity: bulk and localized contributions

We study the expansion near roots of unity of the superconformal index of 4d SU(N) \U0001d4a9 = 4 SYM. In such an expansion, middle-dimensional walls of non-analyticity are shown to emerge in the complex analytic extension of the integrand. These walls intersect the integration contour at infinitesimal vicinities and come from both, the vector and chiral multiplet contributions, and combinations thereof. We will call these intersections vector and chiral bits, and the complementary region bulk, and show that, in the corresponding limit, the integrals along the infinitesimal bits include, among other contributions, factorized products of either Chern-Simons and 3d topologically twisted partition functions.In particular, we find that the leading asymptotic contribution to the index, which comes from collecting all contributions coming from vector bits, reduces to an average over a set of N copies of three-dimensional SU(N) Chern-Simons partition functions in Lens spaces L(m, 1) with m > 1, in the presence of background {mathbb{Z}}_m^{N-1} flat connections. The average is taken over the background connections, which are the positions of individual vector bits along the contour. We also find there are other subleading contributions, a finite number of them at finite N, which include averages over products of Chern-Simons and/or topologically A-twisted Chern-Simons-matter partition functions in three-dimensional manifolds. This shows how in certain limits the index of 4d SU(N) \U0001d4a9 = 4 SYM organizes, via an unambiguously defined coarse graining procedure, into averages over a finite number of lower dimensional theories.

On continuous 2-category symmetries and Yang-Mills theory

We study a 4d gauge theory U(1)N−1 ⋊ SN obtained from a U(1)N−1 theory by gauging a 0-form symmetry SN. We show that this theory has a global continuous 2-category symmetry, whose structure is particularly rich for N > 2. This example allows us to draw a connection between the higher gauging procedure and the difference between local and global fusion, which turns out to be a key feature of higher categorical symmetries. By studying the spectrum of local and extended operators, we find a mapping with gauge invariant operators of 4d SU(N) Yang-Mills theory. The largest group-like subcategory of the non-invertible symmetries of our theory is a {mathbb{Z}}_N^{(1)} 1-form symmetry, acting on the Wilson lines in the same way as the center symmetry of Yang-Mills theory does. Supported by a path-integral argument, we propose that the U(1)N−1 ⋊ SN gauge theory has a relation with the ultraviolet limit of SU(N) Yang-Mills theory in which all Gukov-Witten operators become topological, and form a continuous non-invertible 2-category symmetry, broken down to the center symmetry by the RG flow.

Higher form symmetries TFT in 6d

Symmetries and anomalies of a d-dimensional quantum field theory are often encoded in a (d + 1)-dimensional topological action, called symmetry topological field theory (TFT). We derive the symmetry TFT for the 2-form and 1-form symmetries of 6d (1, 0) field theories, focusing on theories with a single tensor multiplet (rank 1). We implement this by coupling the low-energy tensor branch action to the background fields for the higher-form symmetries and by looking at the symmetry transformation rules on dynamical and background fields. These transformation rules also imply a mixing of the higher-form symmetries in a 3-group structure. For some specific and related higher rank cases, we also derive the symmetry TFT from the holographic dual IIA supergravity solutions. The symmetry TFT action contains a coupling between the 2-form symmetry and the 1-form symmetry backgrounds, which leads to a mixed anomaly between the 1-form symmetries of the 5d KK-theory obtained by circle compactification. We confirm this by a pure 5d analysis provided by the 5d effective low-energy Coulomb branch Lagrangian coupled to background fields. We also derive the symmetry TFT for 5d SU(p) supersymmetric gauge theories with Chern-Simons level q and for 5d theories without non-abelian gauge theory description at low-energy. Finally, we discuss the fate of the 2-form and 1-form symmetry of rank 1 6d field theories when coupled to gravity.

Quantum phases of 4d SU(N) mathcal{N} = 4 SYM

It is argued that 4d SU(N) mathcal{N} = 4 SYM has an accumulation line of zero-temperature topologically ordered phases. Each of these phases corresponds to N bound states charged under electromagnetic {mathbb{Z}}_N^{(1)} one-form symmetries. Each of the N bound states is made of two Dyonic flux components each of them extended over a two dimensional surface. They are localized at the fixed loci of a rotational action, and are argued to correspond to conformal blocks (or primaries) of an SU(N)1 WZNW model on a two-torus.