Tensions and Luscher Terms for (2+1)-dimensional k-strings from Holographic Models

TL;DR

This paper reviews the status of k-string tensions and Luscher terms in gauge theories and computes the Luscher term for a (2+1)-dimensional SU(N) gauge theory using holographic duality, including quantum fluctuation analysis.

Contribution

It provides a holographic calculation of Luscher terms for (2+1)-dimensional k-strings, incorporating quantum fluctuations of bosonic and fermionic sectors.

Findings

Calculated Luscher term for (2+1)-D SU(N) gauge theory via holography

Analyzed quantum fluctuations of probe D4-brane in supergravity background

Reviewed tensions and Luscher terms in lattice, Hamiltonian, and holographic approaches

Abstract

The leading term for the energy of a bound state of k-quarks and k-antiquarks is proportional to its separation L. These k-string configurations have a Luscher term associated with their quantum fluctuations which is typically a 1/L correction to the energy. We review the status of tensions and Luscher terms in the context of lattice gauge theory, Hamiltonian methods, and gauge/gravity correspondence. Furthermore we explore how different representations of the k-string manifest themselves in the gauge/gravity duality. We calculate the Luscher term for a strongly coupled SU(N) gauge theory in (2+1) dimensions using the gauge/gravity correspondence. Namely, we compute one-loop corrections to a probe D4-brane embedded in the Cvetic, Gibbons, Lu, and Pope supergravity background. We investigate quantum fluctuations of both the bosonic and the fermionic sectors.