Chern-Simons five-form and holographic baryons

Abstract

In the top-down holographic model of QCD based on D4/D8-branes in type IIA string theory and some of the bottom-up models, the low energy effective theory of mesons is described by a five-dimensional Yang-Mills-Chern-Simons theory in a certain curved background with two boundaries. The fivedimensional Chern-Simons term plays a crucial role in reproducing the correct chiral anomaly in fourdimensional massless QCD. However, there are some subtle ambiguities in the definition of the Chern-Simons term for the cases with topologically nontrivial gauge bundles, which include the configurations with baryons. In particular, for the cases with three flavors, it was pointed out by Hata and Murata that the naive Chern-Simons term does not lead to an important constraint on the baryon spectrum, which is needed to pick out the correct baryon spectrum observed in nature. In this paper, we propose a formulation of a well-defined Chern-Simons term which can be used for the cases with baryons, and show that it recovers the correct baryon constraint as well as the chiral anomaly in QCD.

Witten-Veneziano mechanism and pseudoscalar glueball-meson mixing in holographic QCD

“…The term involving C 3 contains the Wess-Zumino-Witten term of the dual gauge theory because F 4 = dC 3 is nonzero in the background [9,33]. The Chern-Simons term is also involved in the U (1) A anomaly of the dual gauge theory, because the C 7 term modifies the equations of motion of the C 1 field which is responsible for the θ parameter.…”

Chern-Weil theorem, Lovelock Lagrangians in critical dimensions, and boundary terms in gravity actions

“…Transgression forms (TFs) have proved to be useful to deal with a number of different physical situations. Originally used to treat the general problem of anomalies in field theory [16][17][18], more recent applications range from the study of anomalies in hydrodynamics in the context of gauge/gravity duality [19] to holographic models of baryons [20].…”

Hyperons and $Θ_s^+$ in Holographic QCD

“…The Hamiltonian (15) can then be diagonalized with the help of the following Bogoliubov transformation…”

“…Light and heavy-light baryons are dual to instantons and instanton-heavy meson bound states in bulk [10][11][12][13][14][15], providing a robust geometrical approach to the multi-body bound state problem. The holographic construction provides a dual realization of the chiral soliton approach and its bound states variants [16,17], without the shortcomings of the derivative expansion.…”