Spinorial discrete symmetries and adjoint structures

Symmetries and Mass Splittings in QCD$_2$ Coupled to Adjoint Fermions

Two dimensional QCD coupled to fermions in the adjoint representation of the gauge group $SU(N)$, a useful toy model of QCD strings, is supersymmetric for a certain ratio of quark mass and gauge coupling constant. Here we study the theory in the vicinity of the supersymmetric point; in particular we exhibit the algebraic structure of the model and show that the mass splittings as one moves away from the supersymmetric point obey a universal relation of the form ${M_i}^2(B)-{M_i}^2(F)=M_iδm+O(δm^3)$. We discuss the connection of this relation to string and quark model expectations and verify it…

带有一个伴随 Dirac 费米子的 QCD$_2$ 的对称性、宇宙和相

Symmetries, Universes and Phases of QCD$_2$ with an Adjoint Dirac Fermion

本文研究了带有一个伴随 Dirac 费米子的 2d $SU(N)$ QCD，证明其无质量理论的 IR 极限可分解为对应不同通量管扇区的多个宇宙，并通过非可逆拓扑线揭示混合反常与解禁闭现象，最终提出了有质量 $SU(2)$ 规范理论的相图及禁闭弦张力。

Global gauge anomalies in coset models of conformal field theory

We study the occurrence of global gauge anomalies in the coset models of two-dimensional conformal field theory that are based on gauged WZW models. A complete classification of the non-anomalous theories for a wide family of gauged rigid adjoint or twisted-adjoint symmetries of WZW models is achieved with the help of Dynkin's classification of Lie subalgebras of simple Lie algebras.

关于旋量分类中隐藏类的一个注记

A note on hidden classes in spinor classification

本文探讨了扩展Lounesto旋量分类的可能性，通过分析所有潜在子类并施加约束以突出最相关者，从而深化对旋量及其理论物理应用的理解。

桥接紫外与红外相的涌现非可逆对称性——以伴随QCD为例

Emergent Non-Invertible Symmetries Bridging UV and IR Phases -- The Adjoint QCD Example

该研究以伴随QCD为例，发现沿重整化群流涌现的非可逆对称性可桥接规范理论的紫外微观自由度与红外孤子性质，并将结果推广到任意色数的规范理论，提出紫外重子算符候选。

Unsharp Degrees of Freedom and the Generating of Symmetries

In quantum theory, real degrees of freedom are usually described by operators which are self-adjoint. There are, however, exceptions to the rule. This is because, in infinite dimensional Hilbert spaces, an operator is not necessarily self-adjoint even if its expectation values are real. Instead, the operator may be merely symmetric. Such operators are not diagonalizable - and as a consequence they describe real degrees of freedom which display a form of "unsharpness" or "fuzzyness". For example, there are indications that this type of operators could arise with the description of space-time at…

Gauging 1-form center symmetries in simple $SU(N)$ gauge theories

Consequences of gauging exact $Z_k^C$ center symmetries in several simple $SU(N)$ gauge theories, where $k$ is a divisor of $N$, are investigated. Models discussed include: the $SU(N)$ gauge theory with $N_f$ copies of Weyl fermions in self-adjoint single-column antisymmetric representation, the well-discussed adjoint QCD, QCD-like theories in which the quarks are in a two-index representation of $SU(N)$, and a chiral $SU(N)$ theory with fermions in the symmetric as well as in anti-antisymmetric representations but without fundamentals. Mixed 't Hooft anomalies between the 1-form $Z_k^C$ symme…

Can fermions save large N dimensional reduction?

This paper explores whether Eguchi-Kawai reduction for gauge theories with adjoint fermions is valid. The Eguchi-Kawai reduction relates gauge theories in different numbers of dimensions in the large $N$ limit provided that certain conditions are met. In principle, this relation opens up the possibility of learning about the dynamics of 4D gauge theories through techniques only available in lower dimensions. Dimensional reduction can be understood as a special case of large $N$ equivalence between theories related by an orbifold projection. In this work, we focus on the simplest case of dimens…

Exact Symmetries and Threshold States in Two-Dimensional Models for QCD

Two-dimensional SU$(N)$ gauge theory coupled to a Majorana fermion in the adjoint representation is a nice toy model for higher-dimensional gauge dynamics. It possesses a multitude of "gluinoball" bound states whose spectrum has been studied using numerical diagonalizations of the light-cone Hamiltonian. We extend this model by coupling it to $N_f$ flavors of fundamental Dirac fermions (quarks). The extended model also contains meson-like bound states, both bosonic and fermionic, which in the large-$N$ limit decouple from the gluinoballs. We study the large-$N$ meson spectrum using the Discret…

Self-DUal SU(3) Chern-Simons Higgs Systems

We explore self-dual Chern-Simons Higgs systems with the local $SU(3)$ and global $U(1)$ symmetries where the matter field lies in the adjoint representation. We show that there are three degenerate vacua of different symmetries and study the unbroken symmetry and particle spectrum in each vacuum. We classify the self-dual configurations into three types and study their properties.

The Phase Structure of Supersymmetric Sp(2N_c) Gauge Theories with an Adjoint

We study the phase structure of N = 1 supersymmetric Sp(2N_c) gauge theories with 2N_f fundamentals, an adjoint, and vanishing superpotential. Using a-maximization, we derive analytic expressions for the values of N_f below which the first several gauge-invariant operators in the chiral ring violate the unitarity bound and become free fields. In doing so we are able to explicitly check previous conjectures about the behavior of this theory made by Luty, Schmaltz, and Terning. We then compare this to an analysis of the first two 'deconfined' dual descriptions based on the gauge groups Sp(2N_f+2…

A group theoretical approach to causal structures and positive energy on spacetimes

This article presents a precise description of the interplay between the symmetries of a quantum or classical theory with spacetime interpretation, and some of its physical properties relating to causality, horizons and positive energy. Our major result is that the existence of static metrics on spacetimes and that of positive energy representations of symmetry groups, are equivalent to the existence of particular Adjoint-invariant convex cones in the symmetry algebras. This can be used to study backgrounds of supergravity and string theories through their symmetry groups. Our formalism is bas…

A New ``Dual'' Symmetry Structure of the KP Hierarchy

A new infinite set of commuting additional (``ghost'') symmetries is proposed for the KP-type integrable hierarchy. These symmetries allow for a Lax representation in which they are realized as standard isospectral flows. This gives rise to a new double-KP hierarchy embedding ``ghost'' and original KP-type Lax hierarchies connected to each other via a ``duality'' mapping exchanging the isospectral and ``ghost'' ``times''. A new representation of 2D Toda lattice hierarchy as a special Darboux-Backlund orbit of the double-KP hierarchy is found and parametrized entirely in terms of (adjoint) eige…