The anisotropic chiral boson

TL;DR

This paper develops a theory of anisotropic chiral bosons with a dynamical exponent z, analyzing its symmetries, algebraic structure, and finite-temperature partition function, connecting it to number theory and extending known conformal field theories.

Contribution

It introduces a novel anisotropic chiral boson model with a nonlocal realization of conformal symmetry and derives its partition function related to number theory.

Findings

The theory reduces to known models in special cases.

The partition function links to partition numbers and number theory.

The model exhibits a nonlocal realization of conformal symmetry.

Abstract

We construct the theory of a chiral boson with anisotropic scaling, characterized by a dynamical exponent $z$, whose action reduces to that of Floreanini and Jackiw in the isotropic case ($z=1$). The standard free boson with Lifshitz scaling is recovered when both chiralities are nonlocally combined. Its canonical structure and symmetries are also analyzed. As in the isotropic case, the theory is also endowed with a current algebra. Noteworthy, the standard conformal symmetry is shown to be still present, but realized in a nonlocal way. The exact form of the partition function at finite temperature is obtained from the path integral, as well as from the trace over $\hat{u}(1)$ descendants. It is essentially given by the generating function of the number of partitions of an integer into $z$-th powers, being a well-known object in number theory. Thus, the asymptotic growth of the number of states at fixed energy, including subleading corrections, can be obtained from the appropriate extension of the renowned result of Hardy and Ramanujan.