In arXiv:0805.0150 [hep-th] and arXiv:0812.2909 [hep-th] a general prescription was presented for the computation of real-time correlation functions using the gauge/gravity duality. I apply this prescription to the specific case of retarded thermal correlation functions and derive the usual ingoing boundary conditions at the horizon for bulk fields. The derivation allows me to clarify various issues, in particular the generalization to higher-point functions and the relevance of including the regions beyond the horizon.
We examine thermal Green's functions of fermionic operators in quantum field theories with gravity duals. The calculations are performed on the gravity side using ingoing Eddington-Finkelstein coordinates. We find that at negative imaginary Matsubara frequencies and special values of the wavenumber, there are multiple solutions to the bulk equations of motion that are ingoing at the horizon and thus the boundary Green's function is not uniquely defined. At these points in Fourier space a line of poles and a line of zeros of the correlator intersect. We analyze these `pole-skipping' points in t…
In this communication, based on our paper http://arxiv.org/abs/1409.4186, we discuss a way of enhancing Gauge/Gravity Duality and response of a dual strongly coupled medium on placing the inhomogeneity on the gravity side.
This is a copy of the 2009 Princeton University thesis which examined various aspects of gauge/gravity duality, including renormalization group flows, phase transitions of the holographic entanglement entropy, and instabilities associated with the breaking of supersymmetry. Chapter 5 contains new unpublished material on various instabilities of the weakly curved non-supersymmetric $AdS_4$ backgrounds of M-theory.
Inspired by the long wave-length limit of topological M-theory, which re-constructs the theory of $3+1$D gravity in the self-dual variables' formulation, we conjecture the existence of a duality between Hilbert spaces, the ${\bf H}$-duality, to unify topological M-theory and loop quantum gravity (LQG). By ${\bf H}$-duality non-trivial gravitational holonomies of the kinematical Hilbert space of LQG correspond to space-like M-branes. The spinfoam approach captures the non-perturbative dynamics of space-like M-branes, and can be claimed to be dual to the S-branes foam. The Hamiltonian constraint…
We demonstrate an equivalence between two integrable flows defined in a polynomial ring quotiented by an ideal generated by a polynomial. This duality of integrable systems allows us to systematically exploit the Korteweg-de Vries hierarchy and its tau-function to propose amplitudes for non-compact topological gravity on Riemann surfaces of arbitrary genus. We thus quantise topological gravity coupled to non-compact topological matter and demonstrate that this phase of topological gravity at N=2 matter central charge larger than three is equivalent to the phase with matter of central charge sm…
Freudenthal duality (F-duality), an anti-involution of charge vectors keep the entropy and attractor solutions invariant for an extremal supersymmetric black hole. In this paper, we analyze the effect of F-duality on the entropy of a near-extremal $STU$ black hole in $\mathcal{N}=2$ ungauged, four-dimensional supergravity. We consider double-extremal black holes, whose attractor solutions are fixed in terms of the black hole charges throughout the moduli space. It is well known that JT gravity governs the dynamics of the near-horizon regions of higher dimensional, near-extremal black holes. Ow…
We study the Thermo-field realization of the duality between the Rindler-AdS higher spin theory and $O(N)$ vector theory. The CFT represents a decoupled pair of free $O(N)$ vector field theories. It is shown how this decoupled domain CFT is capable of generating the connected Rindler-AdS background with the full set of Higher Spin fields.
We introduce the gauge/gravity, or AdS/CFT, correspondence with an eye towards its application to strongly coupled systems. We provide an overview of the duality, including the AdS/CFT dictionary and holographic renormalization. We then discuss simple correlation functions in the context of renormalization group flow geometries, holographic thermodynamics and an application to the phase diagram of QCD, real-time correlators and the shear viscosity of strongly coupled field theories, holographic superconductors, and the application of holographic fermionic response to strange metals. These lect…
We perform an in-depth analysis of the transformation rules under duality for couplings of theories containing multiple scalars, $p$-form gauge fields, linearized gravitons or $(p,1)$ mixed symmetry tensors. Following a similar reasoning to the derivation of the Buscher rules for string background fields under T-duality, we show that the couplings for all classes of aforementioned multi-field theories transform according to one of two sets of duality rules. These sets comprise the ordinary Buscher rules and their higher counterpart; this is a generic feature of multi-field theories in spacetim…
We derive a manifestly duality-symmetric formulation of the action principle for conformal gravity linearized around Minkowski space-time. The analysis is performed in the Hamiltonian formulation, the fourth-order character of the equations of motion requiring the formal treatment of the three-dimensional metric perturbation and the extrinsic curvature as independent dynamical variables. The constraints are solved in terms of two symmetric potentials that are interpreted as a dual three-dimensional metric and a dual extrinsic curvature. The action principle can be written in terms of these fou…
On pq-duality and explicit solutions in $c \le 1$ $2d$ gravity models
本文研究非微扰$c le 1$弦理论精确解的积分表示。一般解由两个函数$W(x)$和$Q(x)$确定，这两个函数在无穷远处分别像$x^p$和$x^q$一样是无穷大的。导出了任意$(p,q)$模型的积分模型，明确地证明了与引力耦合的极小模型的$p-q$对偶性。我们还讨论了弦方程的精确解和约化条件，并给出了几个显式例子。
Doubled $α'$-geometry is the simplest higher-derivative gravitational theory with exact global duality symmetry. We use the double metric formulation of this theory to compute on-shell three-point functions to all orders in $α'$. A simple pattern emerges when comparing with the analogous bosonic and heterotic three-point functions. As in these theories, the amplitudes factorize. The theory has no Gauss-Bonnet term, but contains a Riemann-cubed interaction to second order in $α'$.
We investigate gauge/gravity duality for gauge theories in de Sitter space. More precisely, we study a five-dimensional consistent truncation of type IIB supergravity, which encompasses a wide variety of gravity duals of strongly coupled gauge theories, including the Maldacena-Nunez solution and its walking deformations. We find several solutions of the 5d theory with dS_4 spacetime and nontrivial profiles for (some of) the scalars along the fifth (radial) direction. In the process, we prove that one of the equations of motion becomes dependent on the others, for nontrivial warp factor. This d…
We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing col…
Known as a symmetry of vacuum Maxwell equations, the electric-magnetic duality can be lifted actually to a symmetry of an action. The Lagrangian of this action is written in terms of two vector potentials, one electric and one magnetic, and while it is manifestly invariant under duality rotations, it is not manifestly Lorentz covariant. This duality symmetry exists also in linearized gravity in four dimensions, and can be lifted off shell too. In $d$ dimensions, the link between linearized gravity and its dual can also be seen from the point of view of a parental action. This is defined by a f…
We test the background geometry of the BFSS model using a D4-brane probe. This proves a sensitive test of the geometry and we find excellent agreement with the D4-brane predictions based on the solution of a membrane corresponding to the D4-brane propagating on this background.
小弦论的引力波-它产生了在红外线中受到永久限制的四维理论-还没有被详细研究过。我们在杂化SO（32）和E_8 x E_8弦论的框架下解决了这个问题，通过将杂化五膜包裹在校准的非Kahler分辨锥的两圈上来构造这些背景。与基本的小弦论的变形有关，我们发现了许多在四维空间中保持N = 1超对称性的解析解。这些理论都有非阿贝尔的整体对称性，一般产生于杂种优势矢量束和某些轨道状态。在解耦极限下，我们证明了引力场是由在原点处具有爆破的两圈和三圈的非Kahler流形给出的。我们认为这以下的某些对偶序列，包括M-理论扭转流形在一个中间步骤，这有助于我们构建新的I型规范/引力对偶对。在M-理论对偶框架中，我们还阐明了新的翻转和触发序列。
