Fermionic operator mixing in holographic p-wave superfluids

Journal of High Energy Physics (Impact Factor: 6.11). 05/2010; 2010(5):1-67. DOI: 10.1007/JHEP05(2010)053
Source: arXiv


We use gauge-gravity duality to compute spectral functions of fermionic operators in a strongly-coupled defect field theory
in p-wave superfluid states. The field theory is (3+1)-dimensional N = 4 \mathcal{N} = 4 supersymmetric SU(N

) Yang-Mills theory, in the ’t Hooft limit and with large coupling, coupled to two massless flavors of (2+1)-dimensional N = 4 \mathcal{N} = 4 supersymmetric matter. We show that a sufficiently large chemical potential for a U(1) subgroup of the global SU(2) isospin
symmetry triggers a phase transition to a p-wave superfluid state, and in that state we compute spectral functions for the
fermionic superpartners of mesons valued in the adjoint of SU(2) isospin. In the spectral functions we see the breaking of
rotational symmetry and the emergence of a Fermi surface comprised of isolated points as we cool the system through the superfluid
phase transition. The dual gravitational description is two coincident probe D5-branes in AdS
5 × S
5 with non-trivial worldvolume SU(2) gauge fields. We extract spectral functions from solutions of the linearized equations
of motion for the D5-branes’ worldvolume fermions, which couple to one another through the worldvolume gauge field. We develop
an efficient method to compute retarded Green’s functions from a system of coupled bulk fermions. We also perform the holographic
renormalization of free bulk fermions in any asymptotically Euclidean AdS space.

KeywordsGauge-gravity correspondence-AdS-CFT Correspondence-Brane Dynamics in Gauge Theories

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Available from: Matthias Kaminski, Jan 02, 2014
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    • "In particular, new results for fermionic correlators have been found in models which describe strongly coupled systems that are interesting in view of applications to condensed matter physics [11–14] [15] [16] [17]. Such systems have also been studied from a top-down perspective in [18] [19] or more recently in [20] [21]. This naturally leads to the question if from these correlators we may find universal results which are similar to the universality of η/s. "
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    ABSTRACT: We holographically compute supercharge diffusion constants in supersymmetric field theories, dual to AdS black brane solutions of arbitrary dimension. This includes the extension of earlier work by Kontoudi and Policastro for D3-branes to M2- and M5-brane theories. We consider the case of vanishing chemical potential. In particular, we relate the product of a diffusion constant and the energy density to a universal result for the fermionic absorption cross section. This relation is analogous to the famous proof of universality of $\eta / s$. We calculate the diffusion constants in two different ways: First, the computation is performed via the low frequency, low momentum pole of the correlator of supersymmetry currents. This pole describes the hydrodynamic phonino mode, the massless Goldstone fermion of spontaneous supersymmetry breaking by temperature. Second, the calculation is carried out using the dual transversal mode of the bulk gravitino, with the help of a new Kubo formula. Moreover, we provide some evidence for the applicability of generalized dimensional reduction for fermions when computing the corresponding D$p$-brane diffusion constants.
    Preview · Article · Feb 2013 · Journal of High Energy Physics
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    • "In this case the dual field theory is known explicitly. For example p-wave superfluids [9] [10] [11], Fermi surfaces [12] and the gravity dual of a Quantum Hall Plateau transition [13] were investigated. "
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    ABSTRACT: We construct a supersymmetric generalization of the holographic dual of a fractional topological insulator found in \cite{HoyosBadajoz:2010ac}. This is accomplished by introducing a nontrivial gauge field on the world volume of the probe D7 brane. The BPS equations are derived from the $\kappa$-symmetry transformation of the probe brane. The BPS equations are shown to reduce to two first oder nonlinear partial differential equations. Solutions of the BPS equations correspond to a probe brane configuration which preserves four of the thirty-two supersymmetries of the $AdS_5\times S^5$ background. Solutions of the BPS equations which correspond to a holographic fractional topological insulator are obtained numerically.
    Full-text · Article · Apr 2012 · Physical review D: Particles and fields
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    • "Motivated by these results it is natural to extend them to a top-down setting. Fermion spectral functions using probe branes were studied in [6]. Here we will carry out a top-down analysis for the fermionic supersymmetry current, or " supercurrent " , in the most general class of N = 2 d = 3 SCFTs that have AdS 4 × M duals in either D = 10 or D = 11 supergravity. "
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    ABSTRACT: We carry out the first holographic calculation of a fermionic response function for a strongly coupled d=3 system with an explicit D=10 or D=11 supergravity dual. By considering the supersymmetry current, we obtain a universal result applicable to all d=3 N=2 SCFTs with such duals. Surprisingly, the spectral function does not exhibit a Fermi surface, despite the fact that the system is at finite charge density. We show that it has a phonino pole and at low frequencies there is a depletion of spectral weight with a power-law scaling which is governed by a locally quantum critical point.
    Preview · Article · Dec 2011 · Physical Review Letters
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