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For conformal field theories, it is shown how the Ward identity corresponding to dilatation invariance arises in a Wilsonian setting. In so doing, several points which are opaque in textbook treatments are clarified. Exploiting the fact…
The ability to quantify distinctness of a cluster structure is fundamental for certain simulation studies, in particular for those comparing performance of different classification algorithms. The intrinsic integral measure based on the…
We apply exceptional generalised geometry to the study of exactly marginal deformations of $\mathcal{N}=1$ SCFTs that are dual to generic AdS$_5$ flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal…
Techniques of gauge theory are used to define and compute an invariant of certain diffeomorphisms of 4-manifolds. The invariant vanishes for any diffeomorphism which is smoothly isotopic to the identity. As an application, we give the first…
In this talk the gauge symmetry for Wilsonian flows in pure Yang-Mills theories is discussed. The background field formalism is used for the construction of a gauge invariant effective action. The symmetries of the effective action under…
Covariant quantization of theories based on nonlinear extensions of Lie algebras in 2d is studied by using a generalized Lagrangian BRST formalism. The quantum action is constructed to be invariant under the off--shell nilpotent BRST…
We explore some consequences of the crossing symmetry for defect conformal field theories, focusing on codimension one defects like flat boundaries or interfaces. We study surface transitions of the 3d Ising and other O(N) models through…
This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
Consistent interactions that can be added to a free, Abelian gauge theory comprising a BF model and a finite set of massless real scalar fields are constructed from the deformation of the solution to the master equation based on specific…
We provide an alternative to the gauge covariant horizontality condition which is responsible for the derivation of the nilpotent (anti-)BRST symmetry transformations for the gauge and (anti-)ghost fields of a (3 + 1)-dimensional (4D)…
Superconformal Ward identities are derived for the the four point functions of chiral primary BPS operators for $\N=2,4$ superconformal symmetry in four dimensions. Manipulations of arbitrary tensorial fields are simplified by introducing a…
We study in detail the procedure for obtaining couplings of D-branes to closed string fields by evaluating string theory disc amplitudes. We perform a careful construction of the relevant vertex operators and discuss the effects of…
An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the…
A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field-antifield formalism is developed. It is based on a gauged (involving a…
A superfield version on superspace $(x^\mu,\theta^a)$ is proposed for the $Sp(2)$-- covariant Lagrangian quantization of general gauge theories. The BRST- and antiBRST- transformations are realized on superfields as supertranslations in the…
We establish a quantitative bulk-boundary correspondence in interacting topological insulators by relating many-body topological invariants to characteristic degeneracy structures in the entanglement spectrum. Focusing on generalized…
An explicitly-gauge-invariant expansion in powers of $e/\hbar$ times the magnetic flux density is formally obtained for the density of states (as characterized by the trace of the resolvent $\widehat G$ = $(\omega - \hat h)^{-1}$) of a…
We consider an overdetermined fourth order boundary value problem in which the boundary value of the Laplacian of the solution is prescribed, in addition to the homogeneous Dirichlet boundary condition. It is known that, in the case where…
We study a crack lying along an imperfect interface in an anisotropic bimaterial. A method is devised where known weight functions for the perfect interface problem are used to obtain singular integral equations relating the tractions and…