Closed String Theory Research Articles

Odderon in gauge/string duality

At high energies, elastic hadronic cross sections, such as pp, p, π±p, are dominated by vacuum exchange, which in leading order of the 1/Nc expansion has been identified as the BFKL Pomeron or its strong AdS dual the closed string Reggeized graviton [1]. However the difference of particle anti-particle cross sections are given by a so-called Odderon, carrying C = -1 vacuum quantum numbers identified in weak coupling with odd numbers of exchanged gluons. Here we show that in the dual description the Odderon is the Reggeized Kalb-Ramond field (Bμν) in the Neveu-Schwartz sector of closed string theory. To first order in strong coupling, the high energy contribution of the Odderon is evaluated for = 4 Super Yang-Mills by a generalization of the gravity dual analysis for the Pomeron in ref. [1]. The consequences of confinement on the Odderon are estimated in the confining QCD-like AdS5 hardwall model of Polchinski and Strassler [2].

Inner brane: A D3-brane in Nappi-Witten space from an inner automorphism

Wess-Zumino-Witten (WZW) models are abstract conformal field theories with an infinite-dimensional symmetry which accounts for their integrability, and at the same time they have a sigma-model description of closed-string propagation on group manifolds which, in turn, endows the models with an intuitive geometric meaning. We exploit this dual algebraic and geometric property of WZW models to construct an explicit example of a field-dependent reflection matrix for open strings in the Nappi-Witten model. Demanding the momentum outflow at the boundary to be zero determines a certain combination of the left and right chiral currents at the boundary. This same reflection matrix is obtained algebraically from an inner automorphism, giving rise to a space-filling D-brane. Half of the infinite-dimensional affine Kac-Moody symmetry present in the closed-string theory is preserved by this unique combination of the left and the right chiral currents. The operator-product expansions of these boundary currents are computed explicitly and they are shown to obey the same current algebra as those of the closed-string chiral currents. Different choices of the inner automorphisms correspond to different background gauge field configurations. Only those B-field configurations, and the corresponding D-branes, that preserve the diagonal part of the infinite-dimensional chiral algebras are allowed. In this way the existence of the D-branes in curved spaces is further constrained by the underlying symmetry of the ambient spacetime.

Higher-loop amplitudes in the non-minimal pure spinor formalism

We analyze the properties of the non-minimal pure spinor formalism. We show that Siegel gauge on massless vertex operators implies the primary field constraint and the level-matching condition in closed string theory by reconstructing the integrated vertex operator representation from the unintegrated ones. The pure spinor integration in the non-minimal formalism needs a regularisation. To this end we introduce a new regulator for the pure spinor integration and an extension of the regulator to allow for the saturation of the fermionic d-zero modes to all orders in perturbation. We conclude with a preliminary analysis of the properties of the four-graviton amplitude to all genus order.

Investigating the off-shell stability of anti-de Sitter space in string theory

We propose an investigation of stability of vacua in string theory by studying their stability with respect to a (suitable) world-sheet renormalization group (RG) flow. We prove the geometric stability of (Euclidean) anti-de Sitter (AdS) space (i.e., Hn) with respect to the simplest RG flow in closed string theory, the Ricci flow. AdS space is not a fixed point of the Ricci flow. We therefore choose an appropriate flow for which it is a fixed point, prove a linear stability result for AdS space with respect to this flow and then show that this implies its geometric stability with respect to the Ricci flow. The techniques used can be generalized to RG flows involving other fields. We also discuss tools from the mathematics of geometric flows that can be used to study stability of string vacua.

Non-Abelian D-branes, open strings, and gauge theory

There is a subtle difference between the open string dynamics determined by the original dual resonance models and that determined by D-brane constructions within critical closed string theory. For instance, in contrast to the former, the latter have massless scalars in addition to the massless gluon shared by both. We introduce and explain the concept of non-Abelian D-branes, which illuminates this distinction. We employ this concept to offer new possibilities for string duals for large $N$ QCD (pure Yang-Mills gauge theory).

Subcritical string and largeNQCD

We pursue the possibility of using subcritical string theory in 4 spacetime dimensions to establish a string dual for large $N$ QCD. In particular we study the even G-parity sector of the 4 dimensional Neveu-Schwarz dual resonance model as the natural candidate for this string theory. Our point of view is that the open string dynamics given by this model will determine the appropriate subcritical closed string theory, a tree level background of which should describe the sum of planar multiloop open string diagrams. We examine the one-loop open string diagram, which contains information about the closed string spectrum at weak coupling. Higher loop open string diagrams will be needed to determine closed string interactions. We also analyze the field theory limit of the one-loop open string diagram and recover the correct running coupling behavior of the limiting gauge theory.

Nonperturbative deformation of D-brane states by the world sheet noncommutativity

By introducing the noncommutativity in the world sheet, we discuss a modification of the D-brane states in the closed string theory. In particular we show how the world sheet noncommutativity induces a nonperturbative effect to the D-brane states.

On dimer models and closed string theories

We study some aspects of the recently discovered connection between dimer models and D-brane gauge theories. We argue that dimer models are also naturally related to closed string theories on non compact orbifolds of 2 and 3, via their twisted sector R charges, and show that perfect matchings in dimer models correspond to twisted sector states in the closed string theory. We also use this formalism to study the combinatorics of some unstable orbifolds of 2.

Non-supersymmetric tachyon-free type-II and type-I closed strings from RCFT

We consider non-supersymmetric four-dimensional closed string theories constructed out of tensor products of N=2 minimal models. Generically such theories have closed string tachyons, but these may be removed either by choosing a non-trivial partition function or a suitable Klein bottle projection. We find large numbers of examples of both types.

Notes on superconformal Chern-Simons-Matter theories

The three dimensional = 2 supersymmetric Chern-Simons theory coupled to matter fields, possibly deformed by a superpotential, give rise to a large class of exactly conformal theories with Lagrangian descriptions. These theories can be arbitrarily weakly coupled, and hence can be studied perturbatively. We study the theories in the large N limit, and compute the two-loop anomalous dimension of certain long operators. Our result suggests that various = 2 U(N) Chern-Simons theories coupled to suitable matter fields are dual to open or closed string theories in AdS4, which are not yet constructed.

D-branes as a bubbling Calabi-Yau

We prove that the open topological string partition function on a D-brane configuration in a Calabi-Yau manifold X takes the form of a closed topological string partition function on a different Calabi-Yau manifold X_b. This identification shows that the physics of D-branes in an arbitrary background X of topological string theory can be described either by open+closed string theory in X or by closed string theory in X_b. The physical interpretation of the ''bubbling'' Calabi-Yau X_b is as the space obtained by letting the D-branes in X undergo a geometric transition. This implies, in particular, that the partition function of closed topological string theory on certain bubbling Calabi-Yau manifolds are invariants of knots in the three-sphere.

Open string attractors

We present a simple example of a supersymmetric attractor mechanism in the purely open string context of D-branes embedded in curved space-time. Our example involves a class of D3-branes embedded in the 2-charge D1-D5 background of type IIB whose worldvolume contains a 2-sphere. Turning on worldvolume fluxes, these branes carry induced (p,q) string charges. Supersymmetric configurations display a flow of the open string moduli towards an attractor solution independent of their asymptotics. The equations governing this mechanism closely resemble the attractor flow equations for supersymmetric black holes in closed string theory. The BPS equations take the form of a gradient flow and describe worldvolume solitons interpolating between an AdS_2 geometry where the two-sphere has collapsed, and an attractor solution with AdS_2 x S^2 geometry. In these limiting solutions, the preserved supersymmetry is enhanced from 4 to 8 supercharges. We also discuss the interpretation of our solutions as intersecting brane configurations placed in the D1-D5 background, as well as the S-duality transformation to the F1-NS5 background.

Non-perturbative planar equivalence and the absence of closed string tachyons

We consider 'orbifold' and 'orientifold' field theories from the dual closed string theory side. We argue that a necessary condition for planar equivalence to hold is the absence of a closed string tachyonic mode in the dual non-supersymmetric string. We analyze several gauge theories on R3xS1. In the specific case of U(N) theories with symmetric/anti-symmetric fermions ('orientifold field theories') the relevant closed string theory is tachyon-free at large compactification radius (due to winding modes), but it develops a tachyonic mode below a critical radius. Our finding is with agreement with field theory expectations of a phase transition from a C-parity violating phase to a C-parity preserving phase as the compactification radius increases. In the case of U(N)xU(N) theories with bi-fundamental matter ('orbifold field theories') a tachyon is always present in the string spectrum, at any compactification radius. We conclude that on R4 planar equivalence holds for 'orientfiold field theories', but fails for 'orbifold field theories' daughters of N=4 SYM and suggest the same for daughters of N=1 SYM. We also discuss examples of SO/Sp gauge theories with symmetric/anti-symmetric fermions. In this case planar equivalence holds at any compactification radius -in agreement with the absence of tachyons in the string dual.

Covariant BRST Quantization of Closed Strings in the pp-Wave Background

We canonically quantize closed string theory in the pp-wave background with a non-zero flux of the three-form field strength by using the covariant BRST operator formalism. In this canonical quantization, we completely construct new covariant free-mode representations, for which it is particularly important to take account of the commutation relations of the zero mode of the light-cone string coordinate X − with other modes. All covariant string coordinates are composed of free modes. Moreover, employing these covariant string coordinates for the energy-momentum tensor, we calculate the anomaly in the Virasoro algebra and determine the number of dimensions of spacetime and the ordering constant from the nilpotency condition of the BRST charge in the pp-wave background.

Wilson Loops and Topological Phases in Closed String Theory

Using covariant phase space formulations for the natural topological invariants associated with the world-surface in closed string theory, we find that certain Wilson loops defined on the world-surface and that preserve topological invariance, correspond to wave functionals for the vacuum state with zero energy. The differences and similarities with the 2-dimensional QED proposed by Schwinger early are discussed.

THE STOYANOVSKY–RIBAULT–TESCHNER MAP AND STRING SCATTERING AMPLITUDES

Recently, Ribault and Teschner pointed out the existence of a one-to-one correspondence between N-point correlation functions for the SL (2,ℂ)k/ SU (2) WZNW model on the sphere and certain set of 2N-2-point correlation functions in Liouville field theory. This result is based on a seminal work by Stoyanovsky. Here, we discuss the implications of this correspondence focusing on its application to string theory on curved backgrounds. For instance, we analyze how the divergences corresponding to worldsheet instantons in AdS3 can be understood as arising from the insertion of the dual screening operator in the Liouville theory side. We also study the pole structure of N-point functions in the 2D Euclidean black hole and its holographic meaning in terms of the Little String Theory. This enables us to interpret the correspondence between CFT's as encoding a LSZ-type reduction procedure. Furthermore, we discuss the scattering amplitudes violating the winding number conservation in those backgrounds and provide a formula connecting such amplitudes with observables in Liouville field theory. Finally, we study the WZNW correlation functions in the limit k → 0 and show that, at the point k = 0, the Stoyanovsky–Ribault–Teschner dictionary turns out to be in agreement with the FZZ conjecture at a particular point of the space of parameters where the Liouville central charge becomes cL = -2. This result makes contact with recent studies on the dynamical tachyon condensation in closed string theory.

On the worldsheet theories of strings dual to free largeNgauge theories

We analyze in detail some properties of the worldsheet of the closed string theories suggested by Gopakumar to be dual to free large N SU(N) gauge theories (with adjoint matter fields). We use Gopakumar's prescription to translate the computation of space-time correlation functions to worldsheet correlation functions for several classes of Feynman diagrams, by explicit computations of Strebel differentials. We compute the worldsheet operator product expansion in several cases and find that it is consistent with general worldsheet conformal field theory expectations. A peculiar property of the construction is that in several cases the resulting worldsheet correlation functions are non-vanishing only on a sub-space of the moduli space (say, for specific relations between vertex positions). Another strange property we find is that for a conformally invariant space-time theory, the mapping to the worldsheet does not preserve the special conformal symmetries, so that the full conformal group is not realized as a global symmetry on the worldsheet (even though it is, by construction, a symmetry of all integrated correlation functions).

Semilocalized instability of the Kaluza–Klein linear dilaton vacuum

The Kaluza–Klein linear dilaton background of the bosonic string and the Scherk–Schwarz linear dilaton background of the superstring are shown to be unstable to the decay of half of spacetime. The decay proceeds via a condensation of a semilocalized tachyon when the circle is smaller than a critical size, and via a semiclassical instanton process when the circle is larger than the critical size. At criticality the two pictures are related by a duality of the corresponding two-dimensional conformal field theories. This provides a concrete realization of the connection between tachyonic and semiclassical instabilities in closed string theory, and lends strong support to the idea that nonlocalized closed string tachyon condensation leads to the annihilation of spacetime.

Thermodynamics of noncritical M-theory and the topological A-model

In [P. Hořava, C.A. Keeler, Noncritical M-theory in 2 + 1 dimensions as a nonrelativistic Fermi liquid, hep-th/0508024], noncritical M-theory for two-dimensional type 0A and 0B strings was defined in terms of a double-scaled theory of nonrelativistic fermions in 2 + 1 dimensions. Here we study this noncritical M-theory at finite temperature. We derive the exact expression for the free energy of its vacuum solution, as a function of a coupling constant g M and the radius R of the thermal circle. We show that at high temperature, the theory is effectively described by another M-theory solution, whose effective loop-counting coupling scales in a novel way characteristic of M-theory, as T 3 . Our calculations further suggest that noncritical M-theory is dual to the closed string theory of the topological A-model on a Calabi–Yau, with the radius R of the Euclidean time circle in M-theory playing the role of the string coupling constant of the A-model. In this correspondence, T-duality on the Euclidean time circle of noncritical M-theory implies an S-duality for the topological A-model.

TIME-DEPENDENT 2D SPACETIMES FROM MATRICES

Solutions of matrix quantum mechanics have been shown to describe time dependent backgrounds in the holographically dual two-dimensional closed string theory. We review some recent work dealing with nontrivial spacetimes which arise in this fashion and discuss aspects of physical phenomena in them. These include spacetimes with spacelike boundaries.