arXiv subjects

I. Bars

Publications and source records attributed to I. Bars.

18 recordsLinked to original sources

arXiv2003

Fermionic Ghosts in Moyal String Field Theory

We complete the construction of the Moyal star formulation of bosonic open string field theory (MSFT) by providing a detailed study of the fermionic ghost sector. In particular, as in the case of the matter sector, (1) we construct a map from Witten's star product to the Moyal product, (2) we propose a regularization scheme which is consistent with the matter sector and (3) as a check of the formalism, we derive the ghost Neumann coefficients algebraically directly from the Moyal product. The latter satisfy the Gross-Jevicki nonlinear relations even in the presence of the regulator, and when the regulator is removed they coincide numerically with the expression derived from conformal field theory. After this basic construction, we derive a regularized action of string field theory in the Siegel gauge and define the Feynman rules. We give explicitly the analytic expression of the off-shell four point function for tachyons, including the ghost contribution. Some of the results in this paper have already been used in our previous publications. This paper provides the technical details of the computations which were omitted there.

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arXiv2003

Analytic Study of Nonperturbative Solutions in Open String Field Theory

We propose an analytic framework to study the nonperturbative solutions of Witten's open string field theory. The method is based on the Moyal star formulation where the kinetic term can be split into two parts. The first one describes the spectrum of two identical half strings which are independent from each other. The second one, which we call midpoint correction, shifts the half string spectrum to that of the standard open string. We show that the nonlinear equation of motion of string field theory is exactly solvable at zeroth order in the midpoint correction. An infinite number of solutions are classified in terms of projection operators. Among them, there exists only one stable solution which is identical to the standard butterfly state. We include the effect of the midpoint correction around each exact zeroth order solution as a perturbation expansion which can be formally summed to the complete exact solution.

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arXiv2002

String Amplitudes from Moyal String Field Theory

We illustrate a basic framework for analytic computations of Feynman graphs using the Moyal star formulation of string field theory. We present efficient methods of computation based on (a) the monoid algebra in noncommutative space and (b) the conventional Feynman rules in Fourier space. The methods apply equally well to perturbative string states or nonperturbative string states involving D-branes. The ghost sector is formulated using Moyal products with fermionic (b,c) ghosts. We also provide a short account on how the purely cubic theory and/or VSFT proposals may receive some clarification of their midpoint structures in our regularized framework.

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arXiv2001

Noncommutative o(N) and usp(2N) algebras and the corresponding gauge field theories

The extension of the noncommutative u*(N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u*(N) can consistently be restricted to o*(N) and usp*(N) algebras that have new mathematical structures. We give explicit fundamental matrix representations of these algebras, through which the formulation for the corresponding noncommutative gauge field theories are obtained. In addition, we present a D-brane configuration with an orientifold which realizes geometrically our algebraic construction, thus embedding the new noncommutative gauge theories in superstring theory in the presence of a constant background magnetic field. Some algebraic generalizations that may have applications in other areas of physics are also discussed.

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arXiv2000

Tachyon Condensation on Noncommutative Torus

We discuss noncommutative solitons on a noncommutative torus and their application to tachyon condensation. In the large B limit, they can be exactly described by the Powers-Rieffel projection operators known in the mathematical literature. The resulting soliton spectrum is consistent with T-duality and is surprisingly interesting. It is shown that an instability arises for any D-branes, leading to the decay into many smaller D-branes. This phenomenon is the consequence of the fact that K-homology for type II von Neumann factor is labeled by R.

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arXiv2000

Non-Commutative Geometry on a Discrete Periodic Lattice and Gauge Theory

We discuss the quantum mechanics of a particle in a magnetic field when its position x^μ is restricted to a periodic lattice, while its momentum p^μ is restricted to a periodic dual lattice. Through these considerations we define non-commutative geometry on the lattice. This leads to a deformation of the algebra of functions on the lattice, such that their product involves a ``diamond'' product, which becomes the star product in the continuum limit. We apply these results to construct non-commutative U(1) and U(M) gauge theories, and show that they are equivalent to a pure U(NM) matrix theory, where N^{2} is the number of lattice points.

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arXiv1999

String Theory on AdS(3) Revisited

We discuss string theory on AdS(3)xS(3)xM(4) with particular emphasis on unitarity and state-operator correspondence. The AdS-CFT correspondence, in the Minkowski signature, is re-examined by taking into account the only allowed unitary representation: the principal series module of the affine current algebra SL(2,R) supplemented with zero modes. Zero modes play an important role in the description of on-shell states as well as of windings in space-time at the AdS(3) boundary. The theory is presented as part of the supersymmetric WZW model that includes the supergroup SU(2/1,1) or OSp(4/2) or D(2,1;α) with central extension k. A free field representation is given and the vertex operators are constructed in terms of free fields in SL(2,R) principal series representation bases that are labeled by position space or momentum space at the boundary of AdS(3). The vertex operators have the correct operator products with the currents and stress tensor, all of which are constructed from free fields, including the subtle zero modes. It is shown that as k goes to infinity, AdS(3) tends to flat 3D-Minkowski space and the AdS(3) vertex operators in momentum space tend to the vertex operators of flat 3D-string theory (furthermore the theory readjusts smoothly in the rest of the dimensions in this limit).

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arXiv1999

Strings, Branes and Two-Time Physics

We generalize the ideas and formalism of Two-Time Physics from particle dynamics to some specific examples of string and p-brane (p >= 1) dynamics. The two-time string or p-brane action can be gauge fixed to produce various one-time string or p-brane actions that are dual to each other under gauge transformations. We discuss the particular gauges that correspond to tensionless strings and p-branes in flat (d-1)+1 spacetime, rigid strings and p-branes in flat (d-1)+1 spacetime, and tensionless strings and p-branes propagating in the AdS_{d-n} x S^n backgrounds.

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arXiv1999

Lifting M-theory to Two-Time Physics

M-theory has different global supersymmetry structures in its various dual incarnations, as characterized by the M-algebra in 11D, the type IIA, type-IIB, heterotic, type-I extended supersymmetries in 10D, and non-Abelian supersymmetries in the AdS_n x S^m backgrounds. We show that all of these supersymmetries are unified within the supersymmetry OSp(1/64), thus hinting that the overall global spacetime symmetry of M-theory is OSp(1/64). We suggest that the larger symmetries contained within OSp(1/64) which go beyond the familiar symmetries, are non-linearly realized hidden symmetries of M-theory. These can be made manifest by lifting 11D M-theory to the formalism of two-time physics in 13D by adding gauge degrees of freedom. We illustrate this idea by constructing a toy M-model on the worldline in 13D with manifest OSp(1/64) global supersymmetry, and a number of new local symmetries that remove ghosts. Some of the local symmetries are bosonic cousins of kappa supersymmetries. The model contains 0-superbrane and p-forms (for p=3,6) as degrees of freedom. The gauge symmetries can be fixed in various ways to come down to a one time physics model in 11D, 10D, AdS_n x S^m, etc., such that the linearly realized part of OSp(1/64) is the global symmetry of the various dual sectors of M-theory.

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arXiv1999

Supersymmetric Two-Time Physics

We construct an Sp(2,R) gauge invariant particle action which possesses manifest space-time SO(d,2) symmetry, global supersymmetry and kappa supersymmetry. The global and local supersymmetries are non-abelian generalizations of Poincare type supersymmetries and are consistent with the presence of two timelike dimensions. In particular, this action provides a unified and explicit superparticle representation of the superconformal groups OSp(N/4), SU(2,2/N) and OSp(8*/N) which underlie various AdS/CFT dualities in M/string theory. By making diverse Sp(2,R) gauge choices our action reduces to diverse one-time physics systems, one of which is the ordinary (one-time) massless superparticle with superconformal symmetry that we discuss explicitly. We show how to generalize our approach to the case of superalgebras, such as OSp(1/32), which do not have direct space-time interpretations in terms of only zero branes, but may be realizable in the presence of p-branes.

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arXiv1998

Gauged Duality, Conformal Symmetry, and Spacetime with Two Times

We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of dimensions. The key is the gauging of the Sp(2) duality symmetry that treats position and momentum (x,p) as a doublet in phase space. As a consequence of the gauging, the Minkowski space-time vectors (x^μ, p^μ) get enlarged by one additional space-like and one additional time-like dimensions to (x^M,p^M). A manifest global symmetry SO(d,2) rotates (x^M,p^M) like d+2 dimensional vectors. The SO(d,2) symmetry of the parent theory may be interpreted as the familiar conformal symmetry of quantum field theory in Minkowski spacetime in one gauge, or as the dynamical symmetry of a totally different physical system in another gauge. Thanks to the gauge symmetry, the theory permits various choices of ``time'' which correspond to different looking Hamiltonians, while avoiding ghosts. Thus we demonstrate that there is a physical role for a spacetime with two times when taken together with a gauged duality symmetry that produces appropriate constraints.

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arXiv1997

Gauge principles for multi-superparticles

We formulate new gauge principles for n supersymmetric particles in a worldline formalism with N supersymmetries. The models provide realizations of the more general supersymmetries that are encountered in sectors of S-theory or Matrix theory, with a superalgebra that involves products of momenta. Due to local gauge and kappa symmetries the n superparticle momenta and N supercharges are constrained. The constraints have solutions only in a space with n timelike dimensions and SO(d+n-2,n) spacetime symmetry. The cases SO(9,1), SO(10,2) and SO(10,3), with one, two and three timelike dimensions respectively, are of special interest. In each case, due to the constraints, the classical motion and quantum theory of each superparticle are equivalent to the physics with a single time-like dimension in an effective 10D superspace with SO(9,1) Lorentz symmetry.

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arXiv1993

Exact Effective Action and Spacetime Geometry in Gauged WZW Models

We present an effective quantum action for the gauged WZW model $G_{-k}/H_{-k}$. It is conjectured that it is valid to all orders of the central extension $(-k)$ on the basis that it reproduces the exact spacetime geometry of the zero modes that was previously derived in the algebraic Hamiltonian formalism. Besides the metric and dilaton, the new results that follow from this approach include the exact axion field and the solution of the geodesics in the exact geometry. It is found that the axion field is generally non-zero at higher orders of $1/k$ even if it vanishes at large $k$. We work out the details in two specific coset models, one non-abelian, i.e. $SO(2,2)/SO(2,1)$ and one abelian, i.e $SL(2,\IR)\otimes SO(1,1)^{d-2}/SO(1,1)$. The simplest case $SL(2,\IR)/\IR$ corresponds to a limit.

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arXiv1992

$SL(2,R)xSU(2)/R^2$ string model in curved spacetime and exact conformal results

Pursuing further the recent methods in the algebraic Hamiltonian approach to gauged WZW models, we apply them to the bosonic SL(2,R) X SU(2)/R^2 model recently investigated by Nappi and Witten. We find the global space and compute the conformally exact metric and dilaton fields to all orders in the $1/k$ expansion. The semiclassical limit $k',k\to \infty$ of our exact results agree with the lowest order perturbation computation which was done in the Lagrangian formalism. We also discuss the supersymmetric type-II and heterotic versions of this model and verify the non-renormalization of $e^Φ\sqrt{-G}$.

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arXiv1992

Conformally Exact Metric and Dilaton in String Theory on Curved Spacetime

Using a Hamiltonian approach to gauged WZW models, we present a general method for computing the conformally exact metric and dilaton, to all orders in the $1/k$ expansion, for any bosonic, heterotic, or type-II superstring model based on a coset $G/H$. We prove the following relations: (i) For type-II superstrings the conformally exact metric and dilaton are identical to those of the non-supersymmetric {\it semi-classical} bosonic model except for an overall renormalization of the metric obtained by $k\to k- g$. (ii) The exact expressions for the heterotic superstring are derived from their exact bosonic string counterparts by shifting the central extension $k\to 2k-h$ (but an overall factor $(k-g)$ remains unshifted). (iii) The combination $e^Φ\sqrt{-G}$ is independent of $k$ and therefore can be computed in lowest order perturbation theory as required by the correct formulation of a conformally invariant path integral measure. The general formalism is applied to the coset models $SO(d-1,2)_{-k}/SO(d-1,1)_{-k}$ that are relevant for string theory on curved spacetime. Explicit expressions for the conformally exact metric and dilaton for the cases $d=2,3,4$ are given. In the semiclassical limit $(k\to \infty)$ our results agree with those obtained with the Lagrangian method up to 1-loop in perturbation theory.

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arXiv1992

Global Analysis of New Gravitational Singularities in String and Particle Theories

We present a global analysis of the geometries that arise in non-compact current algebra (or gauged WZW) coset models of strings and particles propagating in curved space-time. The simplest case is the 2d black hole. In higher dimensions these geometries describe new and much more complex singularities. For string and particle theories (defined in the text) we introduce general methods for identifying global coordinates and give the general exact solution for the geodesics for any gauged WZW model for any number of dimensions. We then specialize to the 3d geometries associated with $SO(2,2)/SO(2,1)$ (and also $SO(3,1)/SO(2,1)$) and discuss in detail the global space, geodesics, curvature singularities and duality properties of this space. The large-small (or mirror) type duality property is reformulated as an inversion in group parameter space. The 3d global space has two topologically distinct sectors, with patches of different sectors related by duality. The first sector has a singularity surface with the topology of ``pinched double trousers". It can be pictured as the world sheet of two closed strings that join into a single closed string and then split into two closed strings, but with a pinch in each leg of the trousers. The second sector has a singularity surface with the topology of ``double saddle", pictured as the world sheets of two infinite open strings that come close but do not touch. We discuss the geodesicaly complete spaces on each side of these surfaces and interpret the motion of particles in physical terms. A cosmological interpretation is suggested and comments are mode on possible physical applications.

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arXiv1991

A Superstring Theory in Four Curved Space-Time Dimensions

Neveu-Schwarz-Ramond type heterotic and type-II superstrings in four dimensional curved space-time are constructed as exact $N=1$ superconformal theories. The tachyon is eliminated with a GSO projection. The theory is based on the N=1 superconformal gauged WZW model for the anti-de Sitter coset $SO(3,2)/SO(3,1)$ with integer central extension $k=5$. The model has dynamical duality properties in its space-time metric that are similar to the large-small ($R\rightarrow 1/R$) duality of tori. To first order in a $1/k$ expansion we give expressions for the metric, the dilaton, the Ricci tensor and their dual generalizations. The curvature scalar has several singularities at various locations in the 4-dimensional manifold. This provides a new singular solution to Einstein's equations in the presence of matter in four dimensions. A non-trivial path integral measure which we conjectured in previous work for gauged WZW models is verified.

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arXiv1991

Generalized Duality and Singular Strings in Higher Dimensions

Deformations of gauged WZW actions are constructed for any pair $(G,H)$ by taking different embeddings of the gauge group $H\subset G$ as it acts on the left and right of the group element $g$. This leads to models that are dual to each other, generalizing the axial/vector duality of the two dimensional black hole manifold. The classical equations are completely solved for any pair $(G,H)$ and in particular for the anti de Sitter string based on $SO(d- 1,2)/SO(d-1,1)$ for which the normal modes are determined. Duality is demonstrated for models that have the same set of normal modes. Concentrating on $SO(2,2)/SO(2,1)$, the metric and dilaton fields of the $d=3$ string as well as some of the dual generalizations are obtained. They have curvature singularities and represent new singular solutions of Einstein's general relativity in three dimensions.

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