Related papers: Modular invariance as completeness

We extend previous work on the perturbative expansion of the Renyi entropy, $S_q$, around $q=1$ for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to…

The problem of finding all possible effective field theories for the quantum Hall effect is closely related to the problem of classifying all possible modular invariant partition functions for the algebra $u(1)^m$, as was argued recently by…

If $\mathbb{F}_{q}$ is a finite field, $C$ is a vector subspace of $\mathbb{F}_{q}^{n}$ (linear code), and $G$ is a subgroup of the group of linear automorphisms of $\mathbb{F}_{q}^{n}$, $C$ is said to be $G$-invariant if $g(C)=C$ for all…

A systematic analysis of the genus two vacuum amplitudes of chiral self-dual conformal field theories is performed. It is explained that the existence of a modular invariant genus two partition function implies infinitely many relations…

Let the finite group $G$ act linearly on the vector space $V$ over the field $k$ of arbitrary characteristic. If $H<G$ is a subgroup the extension of invariant rings $k[V]^G\subset k[V]^H$ is studied using modules of covariants. An example…

This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…

We have examined quantum theories of electric magnetic duality invariant vector fields enjoying classical conformal invariance in 4-dimensional flat spacetime. We extend Dirac's argument about "the conditions for a quantum field theory to…

We consider the 4d superconformal index for ${\cal N}=2$ gauge theories on $S^1 \times L(r,1)$, where $L(r,1)$ is a Lens space. We focus on a one-parameter slice of the three-dimensional fugacity space and in that sector we show S-duality.…

We define an invariant for compact spin manifolds $X$ of dimension $4k$ equipped with a metric $h$ of positive Yamabe invariant on its boundary. The vanishing of this invariant is a necessary condition for the conformal class of $h$ to be…

This is the first of a sequence of papers proving the quantum invariance under ordinary flops over an arbitrary smooth base. In this first part, we determine the defect of the cup product under the canonical correspondence and show that it…

The purpose of this paper is to generalize Zhu's theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights.…

We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…

In holography, the isometry group of the bulk spacetime corresponds to the symmetries of the boundary theory. We thus approach the question of whether (and when) scale invariance in combination with Poincar\'e invariance implies full…

Recently the algebraic structure of gauge-invariant operators in multi-matrix quantum mechanics has been clarified: this space forms a module over a freely generated ring. The ring is generated by a set of primary invariants, while the…

We examine the electric-magnetic duality for a U(1) gauge theory on a general 4-manifold. The partition function for such a theory transforms as a modular form of specific weight. However, in the canonical approach, we show that S-duality,…

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and…

Haag duality is a remarkable property in QFT stating that the commutant of the algebra of observables localized in some region of spacetime is exactly the algebra associated to the causally disconnected region. It is a strong condition on…

The modular data of a modular category $\mathcal{C}$, consisting of the $S$-matrix and the $T$-matrix, is known to be an incomplete invariant of $\mathcal{C}$. More generally, the invariants of framed links and knots defined by a modular…

An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…

The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of…