The CFT of Sen's Formulation of Chiral Gauge Fields

TL;DR

This paper explores Sen's formulation of chiral gauge fields, establishing its relation to conformal field theories, and extends the framework to curved worldsheets and higher-dimensional self-dual gauge fields.

Contribution

It introduces a generalized Sen action on curved worldsheets, relates it to bosonisation, and extends the formulation to higher-dimensional self-dual gauge fields.

Findings

Sen's action describes two chiral scalars with different metric couplings.

The relation between Sen's theory and chiral scalar theory is a form of bosonisation.

The framework extends to self-dual gauge fields in higher dimensions.

Abstract

Sen's action for chiral bosons in 2 dimensions describes two chiral scalars, one of which couples to the physical metric and one of which couples to a flat metric. It has a generalisation in which the flat metric is replaced by an arbitrary second metric and so can be formulated on any curved world-sheet. When the two metrics are equal, the theory reduces to a $\beta \gamma$ system, giving a non-unitary $c=2$ conformal field theory. We argue that the relation between this and the theory of two chiral bosonic scalars of the same chirality can be viewed as a \lq bosonisation'. We show that the standard vertex operators for the chiral scalars are vertex operators and line operators in the Sen formulation and derive the formulation in the Sen theory of correlation functions in the chiral scalar theory. The flat space Sen theory can be coupled to two different world-sheet metrics in such a way that one scalar couples to one metric and the other to the other metric, so obtaining the general formulation with two metrics. In $d=4k+2$ dimensions, the bi-metric action for a $2k$-form gauge field with self-dual field strength reduces, when the two metrics are equal, to a conformal field theory with a $BF$-type action, except that $B$ is a self-dual $d/2$-form and $F$ is a $d/2$-form field strength, $F=dP$. The self-duality of $B$ means that this is not a topological theory but instead represents two self-dual gauge fields. This has a generalisation to a democratic action for $p$-form gauge fields in any dimension.