Neveu-Schwarz Five-branes Research Articles

NS5-brane backgrounds and coset CFT partition functions

Worldsheet string theory is solvable for a variety of backgrounds involving Neveu-Schwarz fivebranes, in terms of gauged nonlinear sigma models on group manifolds. We compute the worldsheet torus partition function of these models, and propose gauging of null isometries as a unifying principle and conceptual framework for this large family of string backgrounds. In the process, we explain how partition functions of asymmetrically gauged Wess-Zumino-Witten models can be computed from the path integral, and organize and systematize various results scattered throughout the literature.

The supersymmetric Neveu-Schwarz branes of non-relativistic string theory

We construct the basic Neveu-Schwarz (NS) brane solutions of non-relativistic string theory using longitudinal T-duality as a solution generating technique. Extending the NS background fields to a supergravity multiplet, we verify that all solutions we find are half-supersymmetric. The two perturbative solutions we find both have an interpretation as the background geometry outside a string-like object. Correspondingly, we refer to these non-Lorentzian backgrounds as winding string and unwound string solution. Whereas the winding string is part of the on-shell spectrum of non-relativistic string theory, the unwound string only makes sense off-shell where it mediates the instantaneous gravitational force. Seen from the nine-dimensional point of view, we find that the winding string solution is sourced by a non-relativistic massive particle and that the unwound string solution is sourced by a massless Galilean particle of zero colour and spin. We explain how these two string solutions fit into a discrete lightcone quantization of string theory. We shortly discuss the basic NS five-brane and Kaluza-Klein monopole solutions and show that they are both half-supersymmetric.

Wrapped fivebranes redux

The near-horizon region of Neveu-Schwarz fivebranes provides interesting examples of gauge/gravity duality. We revisit the structure of wrapped and/or intersecting fivebranes using the tools of null-gauged WZW models in worldsheet string theory, revealing the effective geometry of the fivebrane throat in a variety of examples. Variant gaugings yield linear dilaton fivebrane throats with AdS3 caps, providing a wealth of information about the near-BPS structure of the corresponding spacetime CFT duals.

Theta Series, Wall-Crossing and Quantum Dilogarithm Identities

Motivated by mathematical structures which arise in string vacua and gauge theories with N=2 supersymmetry, we study the properties of certain generalized theta series which appear as Fourier coefficients of functions on a twisted torus. In Calabi-Yau string vacua, such theta series encode instanton corrections from $k$ Neveu-Schwarz five-branes. The theta series are determined by vector-valued wave-functions, and in this work we obtain the transformation of these wave-functions induced by Kontsevich-Soibelman symplectomorphisms. This effectively provides a quantum version of these transformations, where the quantization parameter is inversely proportional to the five-brane charge $k$. Consistency with wall-crossing implies a new five-term relation for Faddeev's quantum dilogarithm $\Phi_b$ at $b=1$, which we prove. By allowing the torus to be non-commutative, we obtain a more general five-term relation valid for arbitrary $b$ and $k$, which may be relevant for the physics of five-branes at finite chemical potential for angular momentum.

Moonshine in fivebrane spacetimes

We consider type II superstring theory on $K3 \times S^1 \times \mathbb{R}^{1,4}$ and study perturbative BPS states in the near-horizon background of two Neveu-Schwarz fivebranes whose world-volume wraps the $K3 \times S^1$ factor. These states are counted by the spacetime helicity supertrace $\chi_2(\tau)$ which we evaluate. We find a simple expression for $\chi_2(\tau)$ in terms of the completion of the mock modular form $H^{(2)}(\tau)$ that has appeared recently in studies of the decomposition of the elliptic genus of K3 surfaces into characters of the N=4 superconformal algebra and which manifests a moonshine connection to the Mathieu group $M_{24}$.

Dynamical vacuum selection in string theory

We study a system of D-branes localized near an intersection of Neveu–Schwarz fivebranes, that is known to exhibit a landscape of supersymmetric and (metastable) supersymmetry breaking vacua. We show that early universe cosmology drives it to a particular long-lived supersymmetry breaking ground state.

Bound states inN= 2 Liouville theory with boundary and deep throat D-branes

We exhibit bound states in the spectrum of non-compact D-branes in N = 2 Liouville conformal field theory. We interpret these states in the study of D-branes in the near-horizon limit of Neveu-Schwarz five-branes spread on a topologically trivial circle. We match semi-classical di-electric and repulsion effects with exact conformal field theory results and describe the fate of D-branes hitting NS5-branes. We also show that the bound states can give rise to massless vector and hyper multiplets in a low-energy gauge theory on D-branes deep inside the throat.

Fivebrane instanton corrections to the universal hypermultiplet

We analyze the Neveu–Schwarz fivebrane instanton in type IIA string theory compactifications on rigid Calabi–Yau threefolds, in the low-energy supergravity approximation. It there appears as a finite action solution to the Euclidean equations of motion of a double-tensor multiplet (dual to the universal hypermultiplet) coupled to N = 2 , D = 4 supergravity. We determine the bosonic and fermionic zero modes, and the single-centered instanton measure on the moduli space of collective coordinates. The results are then used to compute, in the semiclassical approximation, correlation functions that nonperturbatively correct the universal hypermultiplet moduli space geometry of the low-energy effective action. We find that only the Ramond–Ramond sector receives corrections, and we discuss the breaking of isometries due to instantons.

On integrable models from pp-wave string backgrounds

We construct solutions of type IIB supergravity with non-trivial Ramond-Ramond 5-form in ten dimensions by replacing the transverse flat space of pp-wave backgrounds with exact $N=(4,4)$ $c=4$ superconformal field theory blocks. These solutions, which also include a dilaton and (in some cases) an anti-symmetric tensor field, lead to integrable models on the world-sheet in the light-cone gauge of string theory. In one instance we demonstrate explicitly the emergence of the complex sine-Gordon model, which coincides with integrable perturbations of the corresponding superconformal building blocks in the transverse space. In other cases we arrive at the supersymmetric Liouville theory or at the complex sine-Liouville model. For axionic instantons in the transverse space, as for the (semi)-wormhole geometry, we obtain an entire class of supersymmetric pp-wave backgrounds by solving the Killing spinor equations as in flat space, supplemented by the appropriate chiral projections; as such, they generalize the usual Neveu-Schwarz five-brane solution of type IIB supergravity in the presence of a Ramond-Ramond 5-form. We also present some further examples of interacting light-cone models and we briefly discuss the role of dualities in the resulting string theory backgrounds.

Worldsheet Descriptions of Wrapped NS Five-Branes

We provide a world-sheet description of Neveu-Schwarz five-branes wrapped on a complex projective space. It is an orbifold of the product of an N=2 minimal model and the IR fixed point of a certain linear sigma model. We show how the naked singularity in the supergravity description is resolved by the world-sheet CFT. Applying mirror symmetry, we show that the low-energy theory of NS5-branes wrapped on CP^1 in Eguchi-Hanson space is described by the Seiberg-Witten prepotential for N=2 super-Yang-Mills, with the gauge group given by the ADE-type of the five-brane. The world-sheet CFT is generically regular, but singularities develop precisely at the Argyres-Douglas points and massless monopole points of the space-time theory. We also study the low-energy theory of NS5-branes wrapped on CP^2 in a Calabi-Yau 3-fold and its relation to (2,2) super-Yang-Mills theory in two dimensions.

Noncommutative tachyons and K-theory

We show that the relation between D-branes and noncommutative tachyons leads very naturally to the relation between D-branes and K-theory. We also discuss some relations between D-branes and K-homology, provide a noncommutative generalization of the ABS construction, and give a simple physical interpretation of Bott periodicity. In addition, a framework for constructing Neveu–Schwarz fivebranes as noncommutative solitons is proposed.

Brane transmutation in supergravity

We study a family of BPS solutions of type IIA supergravity that can be interpreted as describing the `transmutation' of a Neveu-Schwarz five-brane into a D4-brane in the presence of a D6-brane. The D4-brane, which terminates on the D6-brane, can be equally well interpreted as a `pure multipole' configuration of NS5-brane wrapped tightly around the D6-brane. Such a transmutation is a "near-core" version (i.e., near the D6-brane) of the brane-creation that can occur when two branes pass through each other, as in the Hanany-Witten construction. The work below highlights certain charge non-conservation features of type IIA supergravity.

String theory in magnetic monopole backgrounds

We discuss string propagation in the near-horizon geometry generated by Neveu-Schwarz fivebranes, Kaluza-Klein monopoles and fundamental strings. When the fivebranes and KK monopoles are wrapped around a compact four-manifold M , the geometry is AdS 3 × S 3/ Z N × M and the space-time dynamics is expected to correspond to a local two-dimensional conformal field theory. We determine the moduli space of space-time CFT's, study the spectrum of the theory and compare the chiral primary operators obtained in string theory to supergravity expectations.

Neveu-Schwarz five-branes at orbifold singularities and holography

We consider Type IIB Neveu-Schwarz five-branes transverse to C 2/ Z n orbifolds and conjecture that string theory on the near horizon geometry is dual to the decoupled theory on the branes. We analyze the conformal field theory describing the near horizon region and the world volume non-critical string theory. The modular invariance consistency condition of string theory is exactly reproduced as the gauge anomaly cancellation condition in the little string theories. We comment on aspects of the holographic nature of this duality.

The Neveu-Schwarz five-brane and its dual geometries

In this paper we discuss two aspects of duality transformations on the Neveu-Schwarz (NS) 5-brane solutions in type II and heterotic string theories. First we demonstrate that the non-extremal NS 5-brane background is U-dual to its CGHS limit, a two-dimensional black hole times $S^3\times T^5$; an intermediate step is provided by the near horizon geometry which is given by the three-dimensional $BTZ_3$ black hole (being closely related to $AdS_3$) times $S^3\times T^4$. In the second part of the paper we discuss the T-duality between $k$ NS 5-branes and the Taub-NUT spaces respectively ALE spaces, which are related to the resolution of the $A_{k-1}$ singularities of the non-compact orbifold ${\bf C}^2/{\bf Z}_{k}$. In particular in the framework of N=1 supersymmetric gauge theories related to brane box constructions we give the metric dual to two sets of intersecting NS 5-branes. In this way we get a picture of a dual orbifold background ${\bf C}^3/ \Gamma$ which is fibered together out of two N=2 models ($\Gamma={\bf Z}_k\times {\bf Z}_{k'}$). Finally we also discuss the intersection of NS 5-branes with D branes, which can serve as probes of the dual background spaces.

Partition functions, duality and the tube metric

The partition function of type IIA and B strings on R 6 × K3 , in the T 4/ Z 2 orbifold limit, is explicitly computed as a modular invariant sum over spin structures required by perturbative unitarity in order to extend the analysis to include type II strings on R6 × W4 , where W4 is associated with the tube metric conformal field theory, given by the degrees of freedom transverse to the Neveu-Schwarz fivebrane solution. This generates partition functions and perturbative spectra of string theories in six space-time dimensions, associated with the modular invariants of the level- k affine SU(2) Kac-Moody algebra. These theories provide a conformal field theory (i.e. perturbative) probe of non-perturbative (fivebrane) vacua. We contrast them with theories whose N = (4, 4) sigma-model action contains n H = k + 2 hypermultiplets as well as vector supermultiplets, and where k is the level just mentioned. In Appendix B we also give a D = 6, N = (1, 1) ‘free fermion’ string model which has. a different moduli space of vacua from the 81-parameter space relevant to the above examples.

M(ore) on chiral gauge theories from D-branes

We consider a brane configuration consisting of intersecting Neveu-Schwarz five-branes, Dirichlet four-branes, and an orientifold four-plane in a C 2/ Z 3 orbifold background. We show that the low-energy dynamics is described by a four-dimensional gauge theory with N = 1 supersymmetry and S( N + 4) × SU( N) or SP(2 M) × SU(2 M) × SU(2 M + 4) gauge symmetry. The matter content of this theory is chiral. In particular, the SU group has one matter field in the antisymmetric tensor or symmetric tensor representation and several fields in the fundamental and antifundamental representations. We discuss various consistency checks on these theories. By considering the brane configuration in M-theory we deduce the spectral curves for these theories. Finally, we consider the effects of replacing the orbifold background with a non-singular ALE space (both with and without an orientifold plane) and show that it leaves the spectral curves unchanged.

Neveu-Schwarz five-branes and Matrix string theory on K3

The Matrix theory description of Type IIA string theory on a compact K3 surface as the theory of Neveu-Schwarz five-branes on $\tilde{K3}\times S^1$ is analyzed. The full multiplet of space-time BPS states is identified in the five-brane world-volume as fluxes.

New curves from branes

We consider configurations of Neveu-Schwarz fivebranes, Dirichlet fourbranes and an orientifold sixplane in type IIA string theory. Upon lifting the configuration to M-theory and proposing a description of how to include the effects of the orientifold sixplane we derive the curves describing the Coulomb branch of N = 2 gauge theories with orthogonal and symplectic gauge groups, product gauge groups of the form ⊗ i SU(k i) ⋇ SO(N) and ⊗ i SU(k i) ⋇ Sp (N) . We also propose new curves describing theories with unitary gauge groups and matter in the symmetric or antisymmetric representation.

Chiral gauge theories from D-branes

We construct brane configurations leading to chiral four dimensional N=1 supersymmetric gauge theories. The brane realizations consist of intersecting Neveu-Schwarz five-branes and Dirichlet four-branes in non-flat spacetime backgrounds. We discuss in some detail the construction in a C^2/Z_M orbifold background. The infrared theory on the four-brane worldvolume is a four dimensional N=1 SU(N)^M gauge theory with chiral matter representations. We discuss various consistency checks and show that the spectral curves describing the Coulomb phase of the theory can be obtained once the orbifold brane construction is embedded in M-theory. We also discuss the addition of extra vectorlike matter and other interesting generalizations.