Related papers: Counting Gauge Invariants: the Plethystic Program
Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue…
We sketch the construction of a gauge invariant Exact Renormalization Group (ERG). Starting from Polchinski's equation, the emphasis is on how a series of ideas have combined to yield the gauge invariant formalism. A novel symmetry of the…
This note presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a…
We show that natural noncommutative gauge theory models on $\mathbb{R}^3_\lambda$ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of $\mathbb{R}^3_\lambda$ and the components of…
We introduce a general approximation scheme in order to calculate gauge invariant observables in the canonical formulation of general relativity. Using this scheme we will show how the observables and the dynamics of field theories on a…
This is the first of two papers in which we study the modular invariance of pseudotraces of logarithmic intertwining operators. We construct and study genus-one correlation functions for logarithmic intertwining operators among generalized…
In this dissertation we discuss various issues concerning application of the Dijkgraaf-Vafa (DV) conjecture to the study of supersymmetric gauge theories. The DV approach is very powerful in that it provides a systematic way of computing…
We review our efforts in investigating gauge theories with fermions in the adjoint representation of the gauge group by means of numerical simulations. These theories have applications in possible extensions of the Standard Model of…
Using the Fredholm setup of [12], we study genus zero (and higher) relative Gromov-Witten invariants with maximum tangency of symplectic log Calabi-Yau fourfolds. In particular, we give a short proof of [23, Conjecture 6.2] that expresses…
We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant…
Using a gauge invariant exact renormalization group, we show how to compute the effective action, and extract the physics, whilst manifestly preserving gauge invariance at each and every step. As an example we give an elegant computation of…
This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or…
The study of entanglement in quantum field theories provides insight into universal properties which are typically challenging to extract by means of local observables. However, calculations of quantities related to entanglement in gauge…
Building on recent work in SU(N) Yang-Mills theory, we construct a manifestly gauge invariant exact renormalization group for QCD. A gauge invariant cutoff is constructed by embedding the physical gauge theory in a spontaneously broken…
We engineer a class of quiver gauge theories with several interesting features by studying D-branes at a simple Calabi-Yau singularity. At weak 't Hooft coupling we argue using field theory techniques that these theories admit both…
It has been understood that correlation functions of multi-trace operators in ${\cal N}=4$ SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand such algebras have been known to…
Motivated by counting pseudo-holomorphic curves in symplectic Calabi-Yau $3$-folds, this article studies a chamber structure in the space of real Cauchy-Riemann operators on a Riemann surface, and constructs three chambered invariants…
There are many applications in gauge theories where the usually employed framework involving gauge-dependent Green's functions leads to considerable problems. In order to overcome the difficulties invariably tied to gauge dependence, we…
Gauge-fixed correlation functions are a valuable tool in intermediate steps when determining gauge-invariant physics. However, when obtaining them in different calculations, it is necessary to use exactly the same definition of the gauge to…
We present a general method for the computation of tree-level superpotentials for the world-volume theory of B-type D-branes. This includes quiver gauge theories in the case that the D-brane is marginally stable. The technique involves…