Related papers: The $\mathcal{N}=2$ Schur index from free fermions
A set of functions is defined which is indexed by a positive integer $n$ and partitions of integers. The case $n=1$ reproduces the standard Schur polynomials. These functions are seen to arise naturally as a determinant of an action on the…
In this article we are concerned with finite dimensional Fermions, by which we mean vectors in a finite dimensional complex space embedded in the exterior algebra over itself. These Fermions are spinless but possess the characterizing…
The Jordan-Wigner transformation is frequently utilised to rewrite quantum spin chains in terms of fermionic operators. When the resulting Hamiltonian is bilinear in these fermions, i.e. the fermions are free, the exact spectrum follows…
We complete a program of study of SU(N) gauge theories coupled to two flavors of fermions in the two-index symmetric representation by performing numerical simulations in SU(4). The beta function, defined and calculated via the…
$SU(N_c)$ lattice gauge theories with $N_f$ flavors of massless staggered fermions are considered at high quark chemical potential $\mu$ and any temperature $T$. In the strong coupling regime (sufficiently small $\beta$) they have been…
We consider a Wilson-Dirac operator with improved chiral properties. We show that, for arbitrarily rough gauge fields, it satisfies the index theorem if we identify the zero modes with the small real eigenvalues of the fermion operator and…
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…
The chiral algebra of a 4D $N\geq2$ superconformal field theory is a vertex operator algebra generated by the Schur subsector of the 4D theory and its rigid (yet rich) structure has been useful in constraining and classifying 4D N=2 SCFTs.…
The general features of the 1/N expansion in statistical mechanics and quantum field theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the…
After deriving inequalities on coefficients arising in the expansion of a Schur $P$-function in terms of Schur functions we give criteria for when such expansions are multiplicity free. From here we study the multiplicity of an irreducible…
We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU($N_c$)…
We present a formulation of domain wall fermions in the Schroedinger functional by following the universality argument given by L\"uscher. To check whether the formulation works, we examine the lowest eigenmode of the free domain wall…
We calculate the free energies $F$ for $U(1)$ gauge theories on the $d$ dimensional sphere of radius $R$. For the theory with free Maxwell action we find the exact result as a function of $d$; it contains the term $\frac{d-4}{2} \log R$…
We compute, in the large $N$ limit, the topologically twisted index of the 3d $T[SU(N)]$ theory, namely the partition function on $\Sigma_{\mathfrak{g}} \times S^1$, with a topological twist on the Riemann surface $\Sigma_{\mathfrak{g}}$.…
We argue that restricted Schur polynomials provide a useful parameterization of the complete set of gauge invariant variables of multi-matrix models. The two point functions of restricted Schur polynomials are evaluated exactly in the free…
We calculate the ultraviolet to infrared evolution and analyze possible types of infrared behavior for several asymptotically free chiral gauge theories with gauge group SU($N$) and massless chiral fermions transforming according to a…
For all 4d $\mathcal{N} = 4$ SYM theories with simple gauge groups $G$, we show that the residues of the integrands in the $\mathcal{N} = 4$ Schur indices, which are related to Gukov-Witten type surface defects in the theories, equal the…
Nonperturbative terms in the free energy of Chern-Simons gauge theory play a key role in its duality to the closed topological string. We show that these terms are reproduced by performing a double scaling limit near the point where the…
We study the supersymmetric partition function on $S^1 \times L(r, 1)$, or the lens space index of four-dimensional $\mathcal{N}=2$ superconformal field theories and their connection to two-dimensional chiral algebras. We primarily focus on…
An expression of the multivariate sigma function associated with a (n,s)-curve is given in terms of algebraic integrals. As a corollary the first term of the series expansion around the origin of the sigma function is directly proved to be…