arXiv subjects

Emil J. Martinec

Publications and source records attributed to Emil J. Martinec.

52 records · Page 3Linked to original sources

arXiv2010

Gravity from the extension of spatial diffeomorphisms

The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential term which can be a general (not necessarily local) functional of the metric. From the perspective of the foundation of Einstein's gravity our results are positive: The extended constraint algebra is either that of Einstein's gravity, or ultralocal gravity. If our goal is a simple modification of Einstein's gravity that for example makes it perturbatively renormalizable, as has recently been suggested, then our results show that there is no such theory within this class.

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arXiv2006

Toward the End of Time

The null-brane space-time provides a simple model of a big crunch/big bang singularity. A non-perturbative definition of M-theory on this space-time was recently provided using matrix theory. We derive the fermion couplings for this matrix model and study the leading quantum effects. These effects include particle production and a time-dependent potential. Our results suggest that as the null-brane develops a big crunch singularity, the usual notion of space-time is replaced by an interacting gluon phase. This gluon phase appears to constitute the end of our conventional picture of space and time.

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arXiv2005

Boundary Ground Ring in Minimal String Theory

We obtain relations among boundary states in bosonic minimal open string theory using the boundary ground ring. We also obtain a difference equation that boundary correlators must satisfy.

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arXiv2004

Matrix Models and 2D String Theory

String theory in two-dimensional spacetime illuminates two main threads of recent development in string theory: (1) Open/closed string duality, and (2) Tachyon condensation. In two dimensions, many aspects of these phenomena can be explored in a setting where exact calculations can be performed. These lectures review the basic aspects of this system.

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arXiv2003

The Annular Report on Non-Critical String Theory

Recent results on the annulus partition function in Liouville field theory are applied to non-critical string theory, both below and above the critical dimension. Liouville gravity coupled to $c\le 1$ matter has a dual formulation as a matrix model. Two well-known matrix model results are reproduced precisely using the worldsheet formulation: (1) the correlation function of two macroscopic loops, and (2) the leading non-perturbative effects. The latter identifies the eigenvalue instanton amplitudes of the matrix approach with disk instantons of the worldsheet approach, thus demonstrating that the matrix model is the effective dynamics of a D-brane realization of $d\le 1$ non-critical string theory. In the context of string theory above the critical dimension, i.e. $d\ge 25$, Liouville field theory realizes two-dimensional de Sitter gravity on the worldsheet. In this case, appropriate D-brane boundary conditions on the annulus realize the S-matrix for two-dimensional de Sitter gravity.

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arXiv2003

Closed String Tachyon Condensation and Worldsheet Inflation

Closed string tachyon condensation in spacetime generates potentials on the worldsheet that model two-dimensional inflationary cosmology. These models illustrate and elucidate a variety of aspects of inflation, in particular the generation of quantum fluctuations and their back-reaction on geometry. We exhibit a class of Liouville gravity models coupled to matter that can exhibit, for example: (a) pure de Sitter gravity; (b) slow-roll inflation; (c) topological inflation; and (d) graceful exit into an FRW phase. The models also provide a quantitative testing ground for ideas about the origin of inflation, such as the various `no-boundary/tunnelling' proposals, and the `eternal/chaotic' inflationary scenario. We suggest an alternative mechanism for quantum creation of cosmological spacetimes which, in the context of the model, provides a natural explanation for why the typical FRW cosmology at large scales underwent a period of inflation at small scale.

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arXiv2002

On Decay of K-theory

Closed string tachyon condensation resolves the singularities of nonsupersymmetric orbifolds, however the resolved space typically has fewer D-brane charges than that of the orbifold. The description of the tachyon condensation process via a gauged linear sigma model enables one to track the topology as one passes from the sigma model's ``orbifold phase'' to its resolved, ``geometric phase,'' and thus to follow how the D-brane charges disappear from the effective spacetime dynamics. As a mathematical consequence, our results point the way to a formulation of a ``quantum McKay correspondence'' for the resolution of toric orbifold singularities.

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arXiv2002

Defects, Decay, and Dissipated States

The worldsheet renormalization group approach to tachyon condensation in string theory is reviewed. The open string case is summarized with examples, and closed string tachyon condensation on nonsupersymmetric orbifolds is examined in detail. The idea that the renormalization group dissipates the localized states associated to the defect is explored.

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arXiv2002

Exciting AdS Orbifolds

The supersymmetric $(AdS_3\times S^3)/Z_N$ orbifold constructed by the authors in hep-th/0106171 is shown to describe AdS fragmentation, where fivebranes are emerging from the F1-NS5 background. The twisted sector moduli of the orbifold are the collective coordinates of groups of $n_5/N$ fivebranes. We discuss the relation between the descriptions of this background as a perturbative string orbifold and as a BPS state in the dual spacetime CFT. Finally, we attempt to apply the lessons learned to the description of BTZ black holes as $AdS_3$ orbifolds and to related big crunch/big bang cosmological scenarios.

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arXiv2001

Localized Tachyons and RG Flows

We study condensation of closed string tachyons living on defects, such as orbifold fixed planes and Neveu-Schwarz fivebranes. We argue that the high energy density of localized states decreases in the process of condensation of such tachyons. In some cases this means that $c_{eff}$ decreases along the flow; in others, $c_{eff}$ remains constant and the decreasing quantity is a closed string analog, $g_{cl}$, of the ``boundary entropy'' of D-branes. We discuss the non-supersymmetric orbifolds $C/Z_n$ and $C^2/Z_n$. In the first case tachyon condensation decreases $n$ and in some cases connects type II and type 0 vacua. In the second case non-singular orbifolds are related by tachyon condensation to both singular and non-singular ones. We verify that $g_{cl}$ decreases in flows between non-singular orbifolds. The main tools in the analysis are the structure of the chiral ring of the perturbed theory, the geometry of the resolved orbifold singularities, and the throat description of singular conformal field theories.

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arXiv2001

Noncommutative Solitons on Orbifolds

In the noncommutative field theory of open strings in a B-field, D-branes arise as solitons described as projection operators or partial isometries in a $C^*$ algebra. We discuss how D-branes on orbifolds fit naturally into this algebraic framework, through the examples of $R^n/G$, $T^n=R^n/Z^n$, and $T^n/G$. We also propose a framework for formulating D-branes on asymmetric orbifolds.

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arXiv2000

D-branes and Strings as Non-commutative Solitons

The non-commutative geometry of a large auxiliary $B$-field simplifies the construction of D-branes as solitons in open string field theory. Similarly, fundamental strings are constructed as localized flux tubes in the string field theory. Tensions are determined exactly using general properties of non-BPS branes, and the non-Abelian structure of gauge fields on coincident D-branes is recovered.

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arXiv1999

Black holes and the phases of brane thermodynamics

Introductory lectures on the relations between the thermodynamics of gauge theory on branes and black holes, including the correspondence principle of Horowitz and Polchinski, the AdS/CFT conjecture, and matrix theory.

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arXiv1998

Conformal Field Theory, Geometry, and Entropy

In the context of the AdS/CFT correspondence, an explicit relation between the physical degrees of freedom of 2+1d gravity and the stress tensor of 1+1d conformal field theory is exhibited. Gravity encodes thermodynamic state variables of conformal field theory, but does not distinguish among different CFT states with the same expectation value for the stress tensor. Simply put, gravity is thermodynamics; gauge theory is statistical mechanics.

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arXiv1998

Matrix Models of AdS Gravity

We explore the connection between anti-deSitter supergravity and gauge theory, in the context of bound states of many D1 and D5 branes. The near-horizon $AdS_3$ supergravity describes the identity sector of the conformal field theory produced by the brane dynamics. A variant of anomaly inflow (for the 2d conformal anomaly) is involved. Dynamical matter fields on $AdS_3$ couple to the chiral ring and its descendant fields on the branes. We propose a map between boundary conformal field theory and bulk supergravity/matter dynamics, which is strongly reminiscent of matrix models of 2d gravity.

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arXiv1997

Comments on Black Holes in Matrix Theory

The recent suggestion that the entropy of Schwarzschild black holes can be computed in matrix theory using near-extremal D-brane thermodynamics is examined. It is found that the regime in which this approach is valid actually describes black strings stretched across the longitudinal direction, near the transition where black strings become unstable to the formation of black holes. It is argued that the appropriate dynamics on the other (black hole) side of the transition is that of the zero modes of the corresponding super Yang-Mills theory. A suggestive mean field theory argument is given for the entropy of black holes in all dimensions. Consequences of the analysis for matrix theory and the holographic principle are discussed.

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