Phase transitions in higher derivative gravity and gauge theory: R-charged black holes

This is a continuation of our earlier work where we constructed a phenomenologically motivated effective action of the boundary gauge theory at finite temperature and finite gauge coupling on $S^3 \times S^1$. In this paper, we argue that this effective action qualitatively reproduces the gauge theory representing various bulk phases of R-charged black hole with Gauss-Bonnet correction. We analyze the system both in canonical and grand canonical ensemble.Comment: 36 pages, 16 figures; v2: typos corrected, references adde

Phase Transitions in Higher Derivative Gravity

This paper deals with black holes, bubbles and orbifolds in Gauss-Bonnet theory in five dimensional anti de Sitter space. In particular, we study stable, unstable and metastable phases of black holes from thermodynamical perspective. By comparing bubble and orbifold geometries, we analyse associated instabilities. Assuming AdS/CFT correspondence, we discuss the effects of this higher derivative bulk coupling on a specific matrix model near the critical points of the boundary gauge theory at finite temperature. Finally, we propose another phenomenological model on the boundary which mimics various phases of the bulk space-time.Comment: 33 pages, 12 figures, LaTeX, typos corrected, clarifications in sections 5 and 6, references adde

Spectral concentration and greedy k-clustering

A popular graph clustering method is to consider the embedding of an input graph into induced by the first k eigenvectors of its Laplacian, and to partition the graph via geometric manipulations on the resulting metric space. Despite the practical success of this methodology, there is limited understanding of several heuristics that follow this framework. We provide theoretical justification for one such natural and computationally efficient variant. Our result can be summarized as follows. A partition of a graph is called strong if each cluster has small external conductance, and large internal conductance. We present a simple greedy spectral clustering algorithm which returns a partition that is provably close to a suitably strong partition, provided that such a partition exists. A recent result shows that strong partitions exist for graphs with a sufficiently large spectral gap between the k-th and (k+1) -st eigenvalues. Taking this together with our main theorem gives a spectral algorithm which finds a partition close to a strong one for graphs with large enough spectral gap. We also show how this simple greedy algorithm can be implemented in near-linear time for any fixed k and error guarantee. Finally, we evaluate our algorithm on some real-world and synthetic inputs

An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion

We apply the theory of algebraic polynomials to analytically study the transonic properties of general relativistic hydrodynamic axisymmetric accretion onto non-rotating astrophysical black holes. For such accretion phenomena, the conserved specific energy of the flow, which turns out to be one of the two first integrals of motion in the system studied, can be expressed as a 8$^{th}$ degree polynomial of the critical point of the flow configuration. We then construct the corresponding Sturm's chain algorithm to calculate the number of real roots lying within the astrophysically relevant domain of $\mathbb{R}$. This allows, for the first time in literature, to {\it analytically} find out the maximum number of physically acceptable solution an accretion flow with certain geometric configuration, space-time metric, and equation of state can have, and thus to investigate its multi-critical properties {\it completely analytically}, for accretion flow in which the location of the critical points can not be computed without taking recourse to the numerical scheme. This work can further be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical system can have in general. We also demonstrate how the transition from a mono-critical to multi-critical (or vice versa) flow configuration can be realized through the saddle-centre bifurcation phenomena using certain techniques of the catastrophe theory.Comment: 19 pages, 2 eps figures, to appear in "General Relativity and Gravitation

Graph Reconstruction via Distance Oracles

We study the problem of reconstructing a hidden graph given access to a distance oracle. We design randomized algorithms for the following problems: reconstruction of a degree bounded graph with query complexity $\tilde{O}(n^{3/2})$; reconstruction of a degree bounded outerplanar graph with query complexity $\tilde{O}(n)$; and near-optimal approximate reconstruction of a general graph

Hagedorn divergences and tachyon potential

We consider the critical behavior for a string theory near the Hagedorn temperature. We use the factorization of the worldsheet to isolate the Hagedorn divergences at all genera. We show that the Hagedorn divergences can be resummed by introducing double scaling limits, which smooth the divergences. The double scaling limits also allow one to extract the effective potential for the thermal scalar. For a string theory in an asymptotic anti-de Sitter (AdS) spacetime, the AdS/CFT correspondence implies that the critical Hagedorn behavior and the relation with the effective potential should also arise from the boundary Yang-Mills theory. We show that this is indeed the case. In particular we find that the free energy of a Yang-Mills theory contains ``vortex'' contributions at finite temperature. Yang-Mills Feynman diagrams with vortices can be identified with contributions from boundaries of moduli space on the string theory side.Comment: 36 pages, 13 figures, uses harvma

Probing the magnetic state by linear and non linear ac magnetic susceptibility measurements in under doped manganite Nd0.8Sr0.2MnO3

We have thoroughly investigated the entire magnetic states of under doped ferromagnetic insulating manganite Nd0.8Sr0.2MnO3 through temperature dependent linear and non linear complex ac magnetic susceptibility measurements. This ferromagnetic insulating manganite is found to have frequency independent ferromagnetic to paramagnetic transition temperature at around 140 K. At around 90 K (\approx T_f) the sample shows a second frequency dependent re - entrant magnetic transition as explored through complex ac susceptibility measurements. Non linear ac susceptibility measurements (higher harmonics of ac susceptibility) have also been performed (with and without the superposition of a dc magnetic field) to further investigate the origin of this frequency dependence (dynamic behavior at this re-entrant magnetic transition). Divergence of 3rd order susceptibility in the limit of zero exciting field indicates a spin glass like freezing phenomena. However, large value of spin relaxation time (?0= 10-8 s) and small value of coercivity (~22 Oe) obtained at low temperature (below T_f) from critical slowing down model and dc magnetic measurements, respectively, are in contrast with what generally observed in a canonical spin glass (?0 = 10-12 - 10-14 s and very large value of coercivity below freezing temperature). We have attributed our observation to the formation of finite size ferromagnetic clusters which are formed as consequence of intrinsic separation and undergo cluster glass like freezing below certain temperature in this under doped manganite. The results are supported by the electronic - and magneto - transport data

Matching gauge theory and string theory in a decoupling limit of AdS/CFT

We identify a regime of the AdS/CFT correspondence in which we can quantitatively match N=4 super Yang-Mills (SYM) for small 't Hooft coupling with weakly coupled type IIB string theory on AdS_5 x S^5. We approach this regime by taking the same decoupling limit on both sides of the correspondence. On the gauge theory side only the states in the SU(2) sector survive, and in the planar limit the Hamiltonian is given by the XXX_{1/2} Heisenberg spin chain. On the string theory side we show that the decoupling limit corresponds to a non-relativistic limit. In this limit some of the bosonic modes and all of the fermionic modes of the string become infinitely heavy and decouple. We first take the decoupling limit of the string sigma-model classically. This enables us to identify a semi-classical regime with semi-classical string states even though we are in a regime corresponding to small 't Hooft coupling. We furthermore analyze the quantum corrections that enter in taking the limit. From this we infer that gauge theory and string theory match, both in terms of the action and the spectrum, for the leading part and the first correction away from the semi-classical regime. Finally we consider the implications for the hitherto unexplained matching of the one-loop contribution to the energy of certain gauge theory and string theory states, and we explain how our results give a firm basis for the matching of the Hagedorn temperature in hep-th/0608115.Comment: 29 pages, 1 figure. v2: Version published in JHEP, section 4 improve