Tachyon-dependent Chern-Simons terms and the V-QCD baryon

Abstract

The structure of the five-dimensional Tachyon-Chern-Simons action and its relevance to single-baryon states in the context of the V-QCD models for holographic QCD with backreacting flavor are analyzed. The most general form of the Tachyon-Chern-Simons 5-form, compatible with symmetries and flavor anomalies is determined. It is the sum of a non-trivial gauge-invariant 5-dimensional form and a non-invariant closed 5-form that reproduces the flavor anomalies. Single-baryon solutions of the gravity theory, arising from the DBI plus Tachyon-Chern-Simons actions are considered. The baryon is realised as a bulk axial instanton. The baryon ansatz and the field equations are derived and the boundary conditions are determined, which ensure that the solution has finite boundary energy and unit baryon charge. The boundary baryon number, which is computed from the universal (closed) part of the Tachyon-Chern-Simons action, is shown to coincide with the bulk axial instanton number.