Abstract
We have recently shown that the ground state of mathcal{N} = 4, SU(Nc) super Yang- Mills coupled to Nf ≪ Nc flavors, in the presence of non-zero isospin and R-symmetry charges, is a supersymmetric, superfluid, color superconductor. The holographic description consists of Nf D7-brane probes in AdS5×S5 with electric and instantonic fields on their worldvolume. These correspond to fundamental strings and D3-branes dissolved on the D7-branes, respectively. Here we use this description to determine the spectrum of mesonic excitations. As expected for a charged superfluid we find non-relativistic, massless Goldstone modes. We also find extra ungapped modes that are not associated to the breaking of any global symmetries but to the supersymmetric nature of the ground state. If the quark mass is much smaller than the scale of spontaneous symmetry breaking a pseudo-Goldstone boson is also present. We highlight some new features that appear only for Nf> 2. We show that, in the generic case of unequal R-symmetry charges, the dissolved strings and D3-branes blow up into a D5-brane supertube stretched between the D7-branes.
Highlights
Interpretation of the gauge theory dynamics by means of the so-called holographic dictionary, a prescription to translate between the QFT and gravity realisations [5, 6]
We have recently shown that the ground state of N = 4, SU(Nc) super YangMills coupled to Nf Nc flavors, in the presence of non-zero isospin and R-symmetry charges, is a supersymmetric, superfluid, color superconductor
We find extra ungapped modes that are not associated to the breaking of any global symmetries but to the supersymmetric nature of the ground state
Summary
= 0, · · · , 7 are worldvolume indices on the D7-branes and collectively denote the xμ and yi directions. The non-Abelian gauge field A takes values in the Lie algebra of SU(2)f. These are SU(2)f-valued, Zα = Zaα σa , and describe the (in general non-commuting) positions of the branes in the zα-directions. The symmetrised-trace over the flavor group, Str, allows one to treat the non-Abelian structures as effectively commuting in the action [33, 34]. As emphasised by the authors of [33, 34] themselves, the action (2.13) is known to be incomplete beyond O( It seems to capture the exact physics for supersymmetric configurations [35, 36]. We will work with (2.19) instead of (2.13)
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