TY - JOUR

T1 - The anisotropic chiral boson

AU - Fuentealba, Oscar

AU - González, Hernán A.

AU - Pino, Miguel

AU - Troncoso, Ricardo

N1 - Funding Information:
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Publisher Copyright:
© 2019, The Author(s).

PY - 2019/11/1

Y1 - 2019/11/1

N2 - We construct the theory of a chiral boson with anisotropic scaling, characterized by a dynamical exponent z that takes positive odd integer values. The 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 û (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 correc- tions, can be obtained from the appropriate extension of the renowned result of Hardy and Ramanujan.

AB - We construct the theory of a chiral boson with anisotropic scaling, characterized by a dynamical exponent z that takes positive odd integer values. The 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 û (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 correc- tions, can be obtained from the appropriate extension of the renowned result of Hardy and Ramanujan.

KW - Conformal and W Symmetry

KW - Field Theories in Lower Dimensions

KW - Space-Time Symmetries

UR - http://www.scopus.com/inward/record.url?scp=85075539177&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2019)123

DO - 10.1007/JHEP11(2019)123

M3 - Article

AN - SCOPUS:85075539177

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 11

M1 - 123

ER -