Jonathan Maltz

Analytic continuation of Liouville theory

A bstractCorrelation functions in Liouville theory are meromorphic functions of the Liouville momenta, as is shown explicitly by the DOZZ formula for the three-point function on S2. In a certain physical region, where a real classical solution exists, the semiclassical limit of the DOZZ formula is known to agree with what one would expect from the action of the classical solution. In this paper, we ask what happens outside of this physical region. Perhaps surprisingly we find that, while in some range of the Liouville momenta the semiclassical limit is associated to complex saddle points, in general Liouville’s equations do not have enough complex-valued solutions to account for the semiclassical behavior. For a full picture, we either must include “solutions” of Liouville’s equations in which the Liouville field is multivalued (as well as being complex-valued), or else we can reformulate Liouville theory as a Chern-Simons theory in three dimensions, in which the requisite solutions exist in a more conventional sense. We also study the case of “timelike” Liouville theory, where we show that a proposal of Al. B. Zamolodchikov for the exact three-point function on S2 can be computed by the original Liouville path integral evaluated on a new integration cycle.

Light States in Chern-Simons Theory Coupled to Fundamental Matter

A bstractMotivated by developments in vectorlike holography, we study SU(N) Chern-Simons theory coupled to matter fields in the fundamental representation on various spatial manifolds. On the spatial torus T2, we find light states at small ‘t Hooft coupling λ = N/k, where k is the Chern-Simons level, taken to be large. In the free scalar theory the gaps are of order

Effective string theory simplified

\sqrt{\lambda }/N

Chaos in matrix models and black hole evaporation

and in the critical scalar theory and the free fermion theory they are of order λ/N. The entropy of these states grows like N log(k). We briefly consider spatial surfaces of higher genus. Based on results from pure Chern-Simons theory, it appears that there are light states with entropy that grows even faster, like N2 log(k). This is consistent with the log of the partition function on the three sphere S3, which also behaves like N2 log(k). These light states require bulk dynamics beyond standard Vasiliev higher spin gravity to explain them.

Deconfinement transition as black hole formation by the condensation of QCD strings

A bstractIn this note we simplify the formulation of the Poincaré-invariant effective string theory in D dimensions by adding an intrinsic metric and embedding its dynamics into the Polyakov formalism. We use this formalism to classify operators order-by-order in the inverse physical length of the string, in a fully gauge-invariant framework. We then use this classification to analyze the universality and nonuniversality of observables, up to and including the second sub-leading order in the long string expansion.

A microscopic description of black hole evaporation via holography

Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question—especially aspects of this question such as a black hole’s negative specific heat—we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. Finally, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.

de Sitter harmonies: Cosmological spacetimes as resonances

We argue that the deconfinement transition of large-N Yang-Mills theory is the condensation of very long and self-intersecting chromo-electric flux strings (QCD string), which is analogous to the formation of a black hole in string theory. We do this by using lattice gauge theory and matrix models. As evidence, we derive an analytic formula for the deconfinement temperature in the strong coupling limit and confirm it numerically. Dual gravity descriptions interpreted in this manner should make it possible to understand the details of the formation of black holes in terms of fundamental strings. We argue that very simple matrix models capture the essence of the formation of black holes.

Toward Holographic Reconstruction of Bulk Geometry from Lattice Simulations

We propose a description of how a large, cold black hole (black zero-brane) in type IIA superstring theory evaporates into freely propagating D0-branes, by solving the dual gauge theory quantitatively. The energy spectrum of emitted D0-branes is parametrically close to thermal when the black hole is large. The black hole, while initially cold, gradually becomes an extremely hot and stringy object as it evaporates. As it emits D0-branes, its emission rate speeds up and it evaporates completely without leaving any remnant. Hence this system provides us with a concrete holographic description of black hole evaporation without information loss.

A proposal of the gauge theory description of the small Schwarzschild black hole in AdS5 × S5

The aim of this work is to provide the details of a calculation summarized in the recent paper by Maltz and Susskind which conjectured a potentially rigorous framework where the status of de Sitter space is the same as that of a resonance in a scattering process. The conjecture is that transition amplitudes between certain states with asymptotically supersymmetric flat vacua contain resonant poles characteristic metastable intermediate states. A calculation employing constrained instantons is presented that illustrates this idea.

de Sitter Space as a Resonance

A bstractA black hole described in SU(N ) gauge theory consists of N D-branes. By separating one of the D-branes from others and studying the interaction between them, the black hole geometry can be probed. In order to obtain quantitative results, we employ the lattice Monte Carlo simulation. As a proof of the concept, we perform an explicit calculation in the matrix model dual to the black zero-brane in type IIA string theory. We demonstrate this method actually works in the high temperature region, where the stringy correction is large. We argue possible dual gravity interpretations.