Papers by Jonathan D Maltz
Physical Review D, 2017
The aim of this work is to provide the details of a calculation summarized in the recent paper by... more 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. Motivations 1 II. de Sitter Space and the Coleman de Luccia Amplitude 2 III. The transition amplitude 4 IV. Regulation of the amplitude and η 0 dependence 5 V. The 1 + 1 dimensional Action in Liouville Gravity 6 VI. The amplitude computation in the context of 3 + 1 dimensions 8 A. Bulk action 8 B. Boundary action 9 C. Corner terms 10 VII. total action and the pole 10 VIII. Discussions and Conclusions 12 Acknowledgments 12 A. Junction Conditions and the constrained Geometry 12 B. Justification For the Integration Region 15 C. geodesics and Christoffells 17 References 18
Effective string theory simplified
Journal of High Energy Physics, 2014
ABSTRACT In this set of notes we simplify the formulation of the Poincar\'e invariant eff... more ABSTRACT In this set of notes we simplify the formulation of the Poincar\'e invariant effective string theory in D dimensions by adding an intrinsic metric and embedding its dynamics into the Polyakov formalism. We apply this formalism to classify operators order by order in the inverse physical length of the string, in a fully gauge-invariant framework. We use this classification to discuss universality and nonuniversalty of observables up to and including next-to-next-to-leading order in the long string expansion.
Journal of High Energy Physics, 2013
Timelike Liouville theory admits the sphere S 2 as a real saddle point, about which quantum fluct... more Timelike Liouville theory admits the sphere S 2 as a real saddle point, about which quantum fluctuations can occur. An issue occurs when computing the expectation values of specific types of quantities, like the distance between points. The problem being that the gauge redundancy of the path integral over metrics is not completely fixed even after fixing to conformal gauge by imposing g µν = e 2 bφ g µν , where φ is the Liouville field and g µν is a reference metric. The physical metric g µν , and therefore the path integral over metrics still possesses a gauge redundancy due to invariance under SL 2 (C) coordinate transformations of the reference coordinates. This zero mode of the action must be dealt with before a perturbative analysis can be made. This paper shows that after fixing to conformal gauge, the remaining zero mode of the linearized Liouville action due to SL 2 (C) coordinate transformations can be dealt with by using standard Fadeev-Popov methods. Employing the gauge condition that the "dipole" of the reference coordinate system is a fixed vector, and then integrating over all values of this dipole vector. The "dipole" vector referring to how coordinate area is concentrated about the sphere; assuming the sphere is embedded in R 3 and centered at the origin, and the coordinate area is thought of as a charge density on the sphere. The vector points along the ray from the origin of R 3 to the direction of greatest coordinate area. A Green's function is obtained and used to compute the expectation value of the geodesic length between two points on the S 2 to second order in the Timelike Liouville coupling b. This quantity doesn't suffer from any power law or logarithmic divergences as a naïve power counting argument might suggest.
Journal of High Energy Physics, 2018
A black hole described in SU(N ) gauge theory consists of N D-branes. By separating one of the D-... more A 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.
International Journal of Modern Physics D, 2016
We propose a description of how a large, cold black hole (black zero-brane) in type IIA superstri... more We propose a description of how a large, cold black hole (black zero-brane) in type IIA superstring theory evaporates into freely propagating [Formula: see text]0-branes, by solving the dual gauge theory quantitatively. The energy spectrum of emitted [Formula: see text]0-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 [Formula: see text]0-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.
Physical Review D, 2014
We argue that the deconfinement transition of large-N Yang-Mills theory is the condensation of ve... more 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.
Physical Review D, 2016
Is the evaporation of a black hole described by a unitary theory? In order to shed light on this ... more 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.
Motivated by developments in vectorlike holography, we study SU(N) Chern-Simons theory coupled to... more Motivated 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 T^2, 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 √(λ)/N 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 N^2 Log(k). This is consistent with the log of the partition function on the three sphere S^3, which also behaves like N^2 Log(k). These light states require bulk dynamics beyond standard Vasiliev higher spin gravity to explain them.
Based on 4d N=4 SYM on R^1×S^3, a gauge theory description of a small black hole in AdS_5×S^5 is ... more Based on 4d N=4 SYM on R^1×S^3, a gauge theory description of a small black hole in AdS_5×S^5 is proposed. The change of the number of dynamical degrees of freedom associated with the emission of the scalar fields' eigenvalues plays a crucial role in this description. By analyzing the microcanonical ensemble, the Hagedorn behavior of long strings at low energy is obtained. Modulo an assumption based on the AdS/CFT duality for a large black hole, the energy of the small ten-dimensional Schwarzschild black hole E∼ 1/(G_ 10,NT^7) is derived. A heuristic gauge theory argument supporting this assumption is also given. The same argument applied to the ABJM theory correctly reproduces the relation for the eleven-dimensional Schwarzschild black hole. One of the consequences of our proposal is that the small and large black holes are very similar when seen from the gauge theory point of view.
Correlation functions in Liouville theory are meromorphic functions of the Liouville momenta, as ... more Correlation 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 the sphere. 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 re...
String theory is arguably the best candidate for a theory of quantum gravity and unified interact... more String theory is arguably the best candidate for a theory of quantum gravity and unified interactions. Reconciling Einstein's theory of General Relativity with Quantum Mechanics. The theory however is best understood on Minkowski and Anti-de Sitter space-times, and not on exponentially expanding space-times with positive cosmological constant, like our own universe. There is still no satisfactory formulation of String Theory on these so called asymptotically de Sitter space times. In this thesis I will discuss certain avenues of progress towards a String Theory formulation of de Sitter space-times. Specifically, how understanding of the analytic continuations of Liouville Theory and how to gauge-fix it in the Timelike regime will aid in the understanding of the proposed FRW-CFT duality of de Sitter space. It is also discussed how non-trivial topology effects proposed Chern-Simons Matter duals of Vasiliev Higher Spin gravity theories which are important in the dS-CFT description of de Sitter Space.
Physical review letters, Jan 10, 2017
A quantum mechanical formulation of de Sitter cosmological spacetimes still eludes string theory.... more A quantum mechanical formulation of de Sitter cosmological spacetimes still eludes string theory. In this Letter we conjecture a potentially rigorous framework in which the status of de Sitter space is the same as that of a resonance in a scattering process. We conjecture that transition amplitudes between certain states with asymptotically supersymmetric flat vacua contain resonant pole characteristic metastable intermediate states. A calculation employing constrained instantons illustrates this idea.
A black hole described in SU(N) gauge theory consists of N D-branes. By separating one of the D-b... more A 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.
The aim of this work is to provided the details of a calculation summarized in the recent paper b... more The aim of this work is to provided 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 being that transition amplitudes between certain states with asymptotically supersymmetric flat vacua contain resonant poles characteristic meta-stable intermediate states. A calculation employing constrained instantons is presented that illustrates this idea. CONTENTS arXiv:1611.03491v1 [hep-th]
A quantum mechanical formulation of de Sitter cosmological spacetimes still eludes string theory.... more A quantum mechanical formulation of de Sitter cosmological spacetimes still eludes string theory. In this paper we conjecture a potentially rigorous framework in which the status of de Sitter space is the same as that of a resonance in a scattering process. We conjecture that transition amplitudes between certain states with asymptotically supersymmetric flat vacua contain resonant poles characteristic meta-stable intermediate states. A calculation employing constrained instantons illustrates this idea.
Based on 4d N = 4 SYM on R 1 ×S 3 , a gauge theory description of a small black hole in AdS 5 ×S ... more Based on 4d N = 4 SYM on R 1 ×S 3 , a gauge theory description of a small black hole in AdS 5 ×S 5 is proposed. The change of the number of dynamical degrees of freedom associated with the emission of the scalar fields' eigenvalues plays a crucial role in this description. By analyzing the microcanonical ensemble, the Hagedorn behavior of long strings at low energy is obtained. Modulo an assumption based on the AdS/CFT duality for a large black hole, the energy of the small ten-dimensional Schwarzschild black hole E ∼ 1/(G 10,N T 7) is derived. A heuristic gauge theory argument supporting this assumption is also given. The same argument applied to the ABJM theory correctly reproduces the relation for the eleven-dimensional Schwarzschild black hole. One of the consequences of our proposal is that the small and large black holes are very similar when seen from the gauge theory point of view.
We propose a description of how a large, cold black hole (black zero-brane) in type IIA superstri... more 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.
Is the evaporation of a black hole described by a unitary theory? In order to shed light on this ... more 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.
In this note we simplify the formulation of the Poincaré-invariant effective string theory in D d... more In 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.
We argue that the deconfinement transition of large-N Yang-Mills theory is the condensation of ve... more 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.
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Papers by Jonathan D Maltz