Holographic glueballs from the circle reduction of Romans supergravity

Abstract

We reconsider a one-parameter class of known solutions of the circle compactification of Romans six-dimensional half-maximal supergravity. The gauge-theory duals of these solutions are confining four-dimensional field theories. Their UV completions consist of the compactification on a circle of a higher-dimensional field theory that is flowing between two fixed points in five dimensions. We systematically study the bosonic fluctuations of the supergravity theory, corresponding to the bosonic glueballs of the dual field theory.We perform numerically the calculation of the spectrum of excitations of all the bosonic fields, several of which had been disregarded in earlier work on the subject. We discuss the results as a function of the one parameter characterising the class of background solutions, hence further extending known results. We show how certain towers of states are independent of the background, and compare these states to existing lattice literature on four-dimensional Yang-Mills (pure) gauge theories, confirming the existence of close similarities.For the aforementioned analysis, we construct gauge-invariant combinations of the fields appearing in the reduction to five dimensions of the supergravity theory, and hence focus on the 32 physical bosonic degrees of freedom. We show explicitly how to implement gaugefixing of the supergravity theory. The results of such technical work could be used to analyse the spectra of other theories proposed in the context of top-down holography. For example, it could be applied to holographic realisations of composite-Higgs and light-dilaton scenarios.

Holographic conformal transition and light scalars

“…There have been previous approaches using holography to understand the conformal transition and the existence of a light dilaton [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. We find however that these studies were not exhaustive nor conclusive.…”

Probing the holographic dilaton

“…We follow the notation in refs. [123,124], and denote by Φ a = {φ, χ} the two active scalars in the five-dimensional reduced theory. A one-parameter family of regular background solutions is known.…”

“…[123] for this whole family, while the full bosonic spectrum of vector, tensor, and other scalar modes has been completed in ref. [124]. The sigma-model kinetic term is given by G ab = diag (2,6).…”

“…We adopt the same conventions and normalisations as in ref. [124]. In addition, we further performed the new calculation of the spectrum of fluctuations of the two scalars φ and χ in the probe approximation.…”

Pseudoscalar glueballs in the Klebanov-Strassler theory

“…As a possible alternative way of testing our equations one can consider the method of [20,27] of deriving the truncated five-dimensional sigma model action for the pseudoscalar fields. A similar work was done in [58] for the dual of the Romans supergravity [59]. It would also be interesting to explicitly derive the pseudoscalar equations from the scalar ones, either using the supersymmetric quantum mechanics approach [23], or the full ten-dimensional supersymmetry transformations.…”