Flavour Fields in Steady State: Stress Tensor and Free Energy

TL;DR

This paper explores the thermodynamics and stress tensor of flavor fields in gauge-string duality with steady-state conditions, revealing universal contributions to free energy and connections to conformal anomalies in various dimensions.

Contribution

It provides a formal framework for analyzing the effective thermodynamics and stress tensor of flavor fields with electric fields and chemical potential, highlighting universal features and scheme-dependence.

Findings

Universal log-divergence coefficient related to conformal anomaly in AdS backgrounds.

Resemblance of the universal factor to heat current in 1+1D conformal field theory.

Vanishing conformal anomaly observed in six-dimensional case.

Abstract

The dynamics of a probe brane in a given gravitational background is governed by the Dirac-Born-Infeld action. The corresponding open string metric arises naturally in studying the fluctuations on the probe. In Gauge-String duality, it is known that in the presence of a constant electric field on the worldvolume of the probe, the open string metric acquires an event horizon and therefore the fluctuation modes on the probe experience an effective temperature. In this article, we bring together various properties of such a system to a formal definition and a subsequent narration of the effective thermodynamics and the stress tensor of the corresponding flavour fields, also including a non-vanishing chemical potential. In doing so, we point out a potentially infinitely-degenerate scheme-dependence of regularizing the free energy, which nevertheless yields a universal contribution in certain cases. This universal piece appears as the coefficient of a log-divergence in free energy when a space-filling probe brane is embedded in AdS$_{d+1}$-background, for $d=2, 4$, and is related to conformal anomaly. For the special case of $d=2$, the universal factor has a striking resemblance to the well-known heat current formula in $(1+1)$-dimensional conformal field theory in steady-state, which endows a plausible physical interpretation to it. Interestingly, we observe a vanishing conformal anomaly in $d=6$.