Abstract:We study the two-point function for fermionic operators in a class of strongly coupled systems using the gauge-gravity correspondence. The gravity description includes a gauge field and a dilaton which determines the gauge coupling and the potential energy. Extremal black brane solutions in this system typically have vanishing entropy. By analyzing a charged fermion in these extremal black brane backgrounds we calculate the two-point function of the corresponding boundary fermionic operator. We find that in some region of parameter space it is of Fermi liquid type. Outside this region no well-defined quasiparticles exist, with the excitations acquiring a non-vanishing width at zero frequency. At the transition, the two-point function can exhibit non-Fermi liquid behaviour.
Extremal black branes are of interest because they correspond to the ground states of field theories at finite charge density in gauge/gravity duality. The geometry of such a brane need not be translationally invariant in the spatial directions along which it extends. A less restrictive requirement is that of homogeneity, which still allows points along the spatial directions to be related to each other by symmetries. In this paper, we find large new classes of homogeneous but anisotropic extremal black brane horizons, which could naturally arise in gauge/gravity dual pairs. In 4 + 1 dimensional spacetime, we show that such homogeneous black brane solutions are classified by the Bianchi classification, which is well known in the study of cosmology, and fall into nine classes. In a system of Einstein gravity with negative cosmological term coupled to one or two massive Abelian gauge fields, we find solutions with an additional scaling symmetry, which could correspond to the nearhorizon geometries of such extremal black branes. These solutions realize many of the Bianchi classes. In one case, we construct the complete extremal solution which asymptotes to AdS space. 4.2 Type VI, III and V 13 4.2.
The exact 2-point function of certain physically motivated operators in SYKlike spin glass models is computed, bypassing the Schwinger-Dyson equations. The models possess an IR low energy conformal window, but our results are exact at all time scales. The main tool developed is a new approach to the combinatorics of chord diagrams, allowing to rewrite the spin glass system using an auxiliary Hilbert space, and Hamiltonian, built on the space of open chord diagrams. We argue the latter can be interpreted as the bulk description and that it reduces to the Schwarzian action in the low energy limit.1 With one important exception : the trace is replaced by some choice of initial and final states.
We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains N Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.
The space of n-point correlation functions, for all possible time-orderings of operators, can be computed by a non-trivial path integral contour, which depends on how many time-ordering violations are present in the correlator. These contours, which have come to be known as timefolds, or out-of-time-order (OTO) contours, are a natural generalization of the Schwinger-Keldysh contour (which computes singly out-of-time-ordered correlation functions). We provide a detailed discussion of such higher OTO functional integrals, explaining their general structure, and the myriad ways in which a particular correlation function may be encoded in such contours. Our discussion may be seen as a natural generalization of the Schwinger-Keldysh formalism to higher OTO correlation functions. We provide explicit illustration for low point correlators (n ≤ 4) to exemplify the general statements. arXiv:1701.02820v4 [hep-th] 10 Dec 2018 Contents C Mathematical details 53 C.1 Proof of Lemma 53 C.2 Proof of Theorem 1 54 C.3 Proof of Theorem 2 55 1We have chosen to phrase the discussion in the context of relativistic QFT emphasizing the distinction between Lorentzian and Euclidean correlators. The analysis however is more broadly applicable, since it distinguishes time-ordered correlators versus unordered ones. The former rely only on the existence of a causal ordering and per se our analysis applies as stated for non-relativistic systems as well.2 The connection between the process of thermalization and out-of-time-order observables dates back to the discussion of [15]. 3 Inspired by these developments, various authors have considered oto correlation functions in a variety of lattice models to probe thermalization and lack thereof (as occurs in many-body localized phases), see [19][20][21][22][23][24][25][26][27][28] for a sampling of these developments. Of related interest are the k-design networks studied in [29,30]. In some of the quantum information literature, one computes an operator average oto correlator which can then be related to Rènyi entropy. See §8 for additional comments. 4 That said, there is an active interest in measurement of such observables; see [31][32][33] for interesting proposals to experimentally measure scrambling and chaos in quantum models using oto observables and tricks to avoid the backwards evolution of the system. See also [34][35][36] for preliminary experiments on this front.
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