Viscosity bound for anisotropic superfluids in higher derivative gravity

In the present paper, based on the principles of gauge/gravity duality we analytically compute the shear viscosity to entropy ratio corresponding to the superfluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note that the ratio indeed receives a finite temperature correction below certain critical temperature. This proves the non universality of shear viscosity to entropy ratio in higher derivative theories of gravity. We also compute the upper bound for the Gauss-Bonnet coupling corresponding to the symmetry broken phase and note that the upper bound on the coupling does not seem to change as long as we are close to the critical point of the phase diagram. However the corresponding lower bound of the shear viscosity to entropy ratio seems to get modified due to the finite temperature effects.Comment: 27 pages; v2: Details added, typos fixed, references updated; version to appear in JHE

Probing analytical and numerical integrability: The curious case of (AdS5×S5)η(AdS_5\times S^5)_{\eta}

Motivated by recent studies related to integrability of string motion in various backgrounds via analytical and numerical procedures, we discuss these procedures for a well known integrable string background $(AdS_5\times S^5)_{\eta}$. We start by revisiting conclusions from earlier studies on string motion in $(\mathbb{R}\times S^3)_{\eta}$ and $(AdS_3)_{\eta}$ and then move on to more complex problems of $(\mathbb{R}\times S^5)_{\eta}$ and $(AdS_5)_{\eta}$. Discussing both analytically and numerically, we deduce that while $(AdS_5)_{\eta}$ strings do not encounter any irregular trajectories, string motion in the deformed five-sphere can indeed, quite surprisingly, run into chaotic trajectories. We discuss the implications of these results both on the procedures used and the background itself.Comment: 31 pages, 3 figures, references updated, analysis for Spiky strings in section (4.1) have been revised, version to appear in JHE

Entanglement entropy from surface terms in general relativity

Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighbourhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1+1 dimensional CFTs at finite temperature whose gravity dual is the BTZ black hole, the Gibbons-Hawking-York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.Comment: 6 pages 1 fig. Essay awarded honourable mention in the Gravity Research Foundation 2013 Awards for Essays on Gravitation. v2: to appear in IJMPD spl. issu

Entanglement entropy in higher derivative holography

We consider holographic entanglement entropy in higher derivative gravity theories. Recently Lewkowycz and Maldacena arXiv:1304.4926 have provided a method to derive the equations for the entangling surface from first principles. We use this method to compute the entangling surface in four derivative gravity. Certain interesting differences compared to the two derivative case are pointed out. For Gauss-Bonnet gravity, we show that in the regime where this method is applicable, the resulting equations coincide with proposals in the literature as well as with what follows from considerations of the stress tensor on the entangling surface. Finally we demonstrate that the area functional in Gauss-Bonnet holography arises as a counterterm needed to make the Euclidean action free of power law divergences.Comment: 24 pages, 1 figure. v3: typos corrected, published versio

Circuit complexity in interacting QFTs and RG flows

We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the $\phi^4$ theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled ground state of the theory. Our approach uses Nielsen's geometric method, which translates into working out the geodesic equation arising from a certain cost functional. We present a general method, making use of integral transforms, to do the required lattice sums analytically and give explicit expressions for the $d=2,3$ cases. Our method enables a study of circuit complexity in the epsilon expansion for the Wilson-Fisher fixed point. We find that with increasing dimensionality the circuit depth increases in the presence of the $\phi^4$ interaction eventually causing the perturbative calculation to breakdown. We discuss how circuit complexity relates with the renormalization group.Comment: 50 pages, 2 figures; references updated; version to appear in JHE