4,558 research outputs found
Novel charges in CFT's
In this paper we construct two infinite sets of self-adjoint commuting
charges for a quite general CFT. They come out naturally by considering an
infinite embedding chain of Lie algebras, an underlying structure that share
all theories with gauge groups U(N), SO(N) and Sp(N). The generality of the
construction allows us to carry all gauge groups at the same time in a unified
framework, and so to understand the similarities among them. The eigenstates of
these charges are restricted Schur polynomials and their eigenvalues encode the
value of the correlators of two restricted Schurs. The existence of these
charges singles out restricted Schur polynomials among the number of bases of
orthogonal gauge invariant operators that are available in the literature.Comment: 58 page
Graph duality as an instrument of Gauge-String correspondence
We explore an identity between two branching graphs and propose a physical
meaning in the context of the gauge-gravity correspondence. From the
mathematical point of view, the identity equates probabilities associated with
, the branching graph of the unitary groups, with probabilities
associated with , the branching graph of the symmetric groups. In
order to furnish the identity with physical meaning, we exactly reproduce these
probabilities as the square of three point functions involving certain
hook-shaped backgrounds. We study these backgrounds in the context of LLM
geometries and discover that they are domain walls interpolating two AdS spaces
with different radii. We also find that, in certain cases, the probabilities
match the eigenvalues of some observables, the embedding chain charges. We
finally discuss a holographic interpretation of the mathematical identity
through our results.Comment: 34 pages. version published in journa
Counting paths with Schur transitions
In this work we explore the structure of the branching graph of the unitary
group using Schur transitions. We find that these transitions suggest a new
combinatorial expression for counting paths in the branching graph. This
formula, which is valid for any rank of the unitary group, reproduces known
asymptotic results. We proceed to establish the general validity of this
expression by a formal proof. The form of this equation strongly hints towards
a quantum generalization. Thus, we introduce a notion of quantum relative
dimension and subject it to the appropriate consistency tests. This new
quantity finds its natural environment in the context of RCFTs and fractional
statistics; where the already established notion of quantum dimension has
proven to be of great physical importance.Comment: 30 pages, 5 figure
- …