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We study correlation functions of D-branes and a supergravity mode in AdS, which are dual to structure constants of two sub-determinant operators with large charge and a BPS single-trace operator. Our approach is inspired by the large charge expansion of CFT and resolves puzzles and confusions in the literature on the holographic computation of correlation functions of heavy operators. In particular, we point out two important effects which are often missed in the literature; the first one is an average over classical configurations of the heavy state, which physically amounts to projecting the state to an eigenstate of quantum numbers. The second one is the contribution from wave functions of the heavy state. To demonstrate the power of the method, we first analyze the three-point functions in $mathcal{N}=4$ super Yang-Mills and reproduce the results in field theory from holography, including the cases for which the previous holographic computation gives incorrect answers. We then apply it to ABJM theory and make solid predictions at strong coupling. Finally we comment on possible applications to states dual to black holes and fuzzballs.
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It has recently been demonstrated that the dynamics of black holes at large $D$ can be recast as a set of non gravitational membrane equations. These membrane equations admit a simple static solution with shape $S^{D-p-2} times R^{p,1}$. In this note we study the equations for small fluctuations about this solution in a limit in which amplitude and length scale of the fluctuations are simultaneously scaled to zero as $D$ is taken to infinity. We demonstrate that the resultant nonlinear equations, which capture the Gregory- Laflamme instability and its end point, exactly agree with the effective dynamical `black brane equations of Emparan Suzuki and Tanabe. Our results thus identify the `black brane equations as a special limit of the membrane equations and so unify these approaches to large $D$ black hole dynamics.
We study extremal and non-extremal generalizations of the regular non-abelian monopole solution of hep-th/9707176, interpreted in hep-th/0007018 as 5-branes wrapped on a shrinking S^2. Naively, the low energy dynamics is pure N=1 supersymmetric Yang-Mills. However, our results suggest that the scale of confinement and chiral symmetry breaking in the Yang-Mills theory actually coincides with the Hagedorn temperature of the little string theory. We find solutions with regular horizons and arbitrarily high Hawking temperature. Chiral symmetry is restored at high energy density, corresponding to large black holes. But the entropy of the black hole solutions decreases as one proceeds to higher temperatures, indicating that there is a thermodynamic instability and that the canonical ensemble is ill-defined. For certain limits of the black hole solutions, we exhibit explicit non-linear sigma models involving a linear dilaton. In other limits we find extremal non-BPS solutions which may have some relevance to string cosmology.
We discuss some general properties of defect branes, i.e. branes of co-dimension two, in (toroidally compactified) IIA/IIB string theory. In particular, we give a full classification of the supersymmetric defect branes in dimensions 2 < D < 11 as well as their higher-dimensionalstring and M-theory origin as branes and a set of generalized Kaluza-Klein monopoles. We point out a relation between the generalized Kaluza-Klein monopole solutions and a particular type of mixed-symmetry tensors. These mixed-symmetry tensors can be defined at the linearized level as duals of the supergravity potentials that describe propagating degrees of freedom. It is noted that the number of supersymmetric defect branes is always twice the number of corresponding central charges in the supersymmetry algebra.
We construct the most general supersymmetric configuration of D2-branes and D6-branes on a 6-torus. It contains arbitrary numbers of branes at relative U(3) angles. The corresponding supergravity solutions are constructed and expressed in a remarkably simple form, using the complex geometry of the compact space. The spacetime supersymmetry of the configuration is verified explicitly, by solution of the Killing spinor equations. Our configurations can be interpreted as a 16-parameter family of regular extremal black holes in four dimensions. Their entropy is interpreted microscopically by counting the degeneracy of bound states of D-branes. Our result agrees in detail with the prediction for the degeneracy of BPS states in terms of the quartic invariant of the E(7,7) duality group.
In this highly speculative note we conjecture that it may be possible to understand features of coincident D-branes, such as the appearance of enhanced non-abelian gauge symmetry, in a purely geometric fashion, using a form of geometry known as scheme theory. We give a very brief introduction to some relevant ideas from scheme theory, and point out how these ideas work in special cases.
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