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From 4d Yang-Mills to 2d ℂℙN − 1 model: IR problem and confinement at weak coupling

We study four-dimensional SU(N) Yang-Mills theory on \( \mathbb{R}\times {\mathbb{T}}^3=\mathbb{R}\times {S}_A^1\times {S}_B^1\times {S}_C^1 \), with a twisted boundary condition by a ℤ N center symmetry imposed on S B 1 × S C 1 . 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...

Dai-Freed theorem and topological phases of matter

We describe a physics derivation of theorems due to Dai and Freed about the Atiyah-Patodi-Singer eta-invariant which is important for anomalies and topological phases of matter. This is done by studying a massive fermion. The key role is played by the wave function of the ground state in the Hilbert space of the fermion in the large mass limit. The ground state takes values in...

8d gauge anomalies and the topological Green-Schwarz mechanism

String theory provides us with 8d supersymmetric gauge theory with gauge algebras \( \mathfrak{s}\mathfrak{u}(N),\mathfrak{s}\mathfrak{o}(2N),\mathfrak{s}\mathfrak{p}(N),{\mathfrak{e}}_6,{\mathfrak{e}}_7\kern0.5em \mathrm{and}\kern0.5em {\mathfrak{e}}_8 \), but no construction for \( \mathfrak{so}\left(2N+1\right) \), \( {\mathfrak{f}}_4 \) and \( {\mathfrak{g}}_2 \) is known. In...

Gauge interactions and topological phases of matter

We study the effects of strongly coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time-reversal symmetry. We first derive a sufficient condition for the introduction of a dynamical Yang–Mills field to preserve the topological phase of matter, and then show how...

Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories

We consider general 5d SU(N ) quiver gauge theories whose nodes form an ADE Dynkin diagram of type G. Each node has SU(N i ) gauge group of general rank, Chern-Simons level κ i and additional w i fundamentals. When the total flavor number at each node is less than or equal to 2N i − 2|κ i |, we give general rules under which the symmetries associated to instanton currents are...

Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills

Kazuya Yonekura 0 0 School of Natural Sciences, Institute for Advanced Study , 1 Einstein Drive, Princeton, NJ 08540 U.S.A Twisted compactification of the 6d N = (2, 0) theories on a punctured

The moduli space of vacua of \( \mathcal{N}=2 \) class \( \mathcal{S} \) theories

We develop a systematic method to describe the moduli space of vacua of four dimensional \( \mathcal{N}=2 \) class \( \mathcal{S} \) theories including Coulomb branch, Higgs branch and mixed branches. In particular, we determine the Higgs and mixed branch roots, and the dimensions of the Coulomb and Higgs components of mixed branches. They are derived by using generalized Hitchin...

6d \( \mathcal{N}=\left(1,\;0\right) \) theories on S 1 /T 2 and class S theories: part II

We study the T 2 compactification of a class of 6d \( \mathcal{N}=\left(1,\;0\right) \) theories that is Higgsable to \( \mathcal{N}=\left(2,\;0\right) \) theories. We show that the resulting 4d \( \mathcal{N}=2 \) theory at the origin of the Coulomb branch and the parameter space is generically given by two superconformal matter sectors coupled by an infrared-free gauge...

Generalized Hitchin system, spectral curve and \( \mathcal{N} \) =1 dynamics

A generalized Hitchin equation was proposed as the BPS equation for a large class of four dimensional \( \mathcal{N} \) = 1 theories engineered using M5 branes. In this paper, we show how to write down the spectral curve for the moduli space of generalized Hitchin equations, and extract interesting \( \mathcal{N} \) = 1 dynamics out of it, such as deformed modui space, chiral...

Mass-deformed T N as a linear quiver

The T N theory is a non-Lagrangian theory with SU(N)3 flavor symmetry. We argue that when mass terms are given so that two of SU(N)’s are both broken to SU(N −1)×U(1), it becomes T N −1 theory coupled to an SU(N −1) vector multiplet together with N fundamentals. This implies that when two of SU(N)’s are both broken to U(1) N −1, the theory becomes a linear quiver. We perform...

6d \( \mathcal{N}=\left(1,0\right) \) theories on T 2 and class S theories. Part I

We show that the \( \mathcal{N}=\left(1,0\right) \) superconformal theory on a single M5 brane on the ALE space of type G = A n , D n , E n , when compactified on T 2, becomes a class S theory of type G on a sphere with two full punctures and a simple puncture. We study this relation from various viewpoints. Along the way, we develop a new method to study the 4d SCFT arising from...

Anomaly polynomial of general 6D SCFTs

We describe a method to determine the anomaly polynomials of general 6D $\mathcal {N}={(2,0)}$ and $\mathcal {N}={(1,0)}$ superconformal field theories (SCFTs), in terms of the anomaly matching on their tensor branches. This method is almost purely field theoretical, and can be applied to all known 6D SCFTs. We demonstrate our method in many concrete examples, including $\mathcal...