NS5-branes Research Articles

Exact half-BPS type IIB interface solutions I: local solution and supersymmetric Janus

The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold AdS4 ? S2 ? S2 ? ? with SO(2, 3) ? SO(3) ? SO(3) symmetry in terms of two holomorphic functions on a Riemann surface ?, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrable system to a linear equation which can be solved exactly. Amongst the infinite class of solutions, a non-singular Janus solution is identified which provides the AdS/CFT dual of the maximally supersymmetric Yang-Mills interface theory discovered recently. The construction of general classes of globally non-singular solutions, including fully back-reacted AdS5 ? S5 and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper [1].

Metric and coupling reversal in string theory

Invariance under reversing the sign of the metric G M N ( x ) and/or the sign of the string coupling field H ( x ) , where 〈 H ( x ) 〉 = g s , leads to four possible universes denoted 1, I , J , K according as ( G , H ) → ( G , H ) , ( − G , H ) , ( − G , − H ) , ( G , − H ) , respectively. Universe 1 is described by conventional string/M theory and contains all M, D, F and NS branes. Universe I contains only D ( − 1 ) , D3 and D7. Universe J contains only D1, D5, D9 and Type I. Universe K contains only F1 and NS5 of IIB and heterotic SO(32).

Semiclassical strings probing NS5 brane wrapped onS5

We study little string theory on R^1 x S^5, defined by a theory which lives on type IIA N NS5 branes wrapped on S^5, using its supergravity dual. In particular we study semiclassical rotating closed strings in this background. We also consider Penrose limit of this background that leads to a plane wave on which string theory is exactly solvable.

COSMOLOGICAL SOLUTION FROM D-BRANE MOTION IN NS5-BRANES BACKGROUND

We study dynamics of a D3-brane propagating in the vicinity of k coincident NS5 branes. We show that when gs is small, there exists a regime in which dynamics of the D-brane is governed by Dirac–Born–Infeld action while higher order derivative in the expansion cannot be neglected. This leads to a restriction on how fast scalar field may roll. We analyze the motion of a rolling scalar field in this regime, and extend the analysis to cosmological systems obtained by coupling this type of field theory to four-dimensional gravity. It also leads to some FRW cosmologies, some of which are related to those obtained with tachyon matter.

D-Brane Dynamics and NS5 Rings

We consider the classical motion of a probe D-brane moving in the background geometry of a ring of NS5 branes, assuming that the latter are non-dynamical. We analyse the solutions to the Dirac-Born-Infield (DBI) action governing the approximate dynamics of the system. In the near horizon (throat) approximation we find several exact solutions for the probe brane motion. These are compared to numerical solutions obtained in more general cases. One solution of particular interest is when the probe undergoes oscillatory motion through the centre of the ring (and perpendicular to it). By taking the ring radius sufficiently large, this solution should remain stable to any stringy corrections coming from open-strings stretching between the probe and the NS5-branes along the ring.

The Supergravity Dual of the BMN Matrix Model

We propose type IIA supergravity solutions dual to the 1/2 BPS vacua of the BMN matrix model. These dual solutions are analyzed using the Polchinski-Strassler method and have brane configurations of concentric shells of D2 branes (or NS5 branes) with various radii and D0 charge. These branes can be viewed as polarized from $N$ D0 branes by a transverse R-R magnetic 6-form flux and an NS-NS 3-form flux. In the region far from branes, the solutions reduce to perturbation around the near horizon geometry of $N$ D0 branes, by turning on these R-R and NS-NS fluxes, which are dual to the deformation of the BFSS matrix model by adding mass terms and the Myers term. The solutions with these additional fluxes preserve 16 supersymmetries. We also briefly discuss these fluxes in the possible supergravity duals of M(atrix) theories on less supersymmetric plane-waves.

Comments on D-brane Dynamics Near NS5-Branes

We study the properties of a D-brane in the presence of $k$ NS5 branes. The Dirac-Born-Infeld action describing the dynamics of this D-brane is very similar to that of a non-BPS D-brane in ten dimensions. As the D-brane approaches the fivebranes, its equation of state approaches that of a pressureless fluid. In non-BPS D-brane case this is considered as an evidence for the decay of the D-brane into ``tachyon matter''. We show that in our case similar behavior is the consequence of the motion of the D-brane. In particular in the rest frame of the moving D-brane the equation of state is that of a usual D-brane, for which the pressure is equal to the energy density. We also compute the total cross-section for the decay of the D-brane into closed string modes and show that the emitted energy has a power like divergence for $D0$, $D1$ and $D2$ branes, while converges for higher dimensional D-branes. We also speculate on the possibility that the infalling D-brane describes a decaying defect in six dimensional Little String Theory.

ExactN=2supergravity solutions with polarized branes

We construct several classes of exact supersymmetric supergravity solutions describing D4 branes polarized into NS5 branes and F-strings polarized into D2 branes. These setups belong to the same universality class as the perturbative solutions used by Polchinski and Strassler to describe the string dual of N=1* theories. The D4-NS5 setup can be interpreted as a string dual to a confining 4+1 dimensional theory with 8 supercharges, whose properties we discuss. By T-duality, our solutions give Type IIB supersymmetric backgrounds with polarized branes.

Probing Orientifold Behavior Near NS Branes

The effect of NS 5 branes on an orientifold is studied. The orientifold is allowed to pass through a pile of k NS branes forming a regularized CHS geometry. Its effect on open strings in its vicinity is used to study the change in the orientifold charge induced by the NS branes.

Brane gas cosmology, M-theory and little string theory

We generalize the Brane Gas Cosmological Scenario to M-theory degrees of freedom, namely $M5$ and $M2$ branes. Without brane intersections, the Brandenberger Vafa(BV) arguments applied to M-theory degrees of freedom generically predict a large 6 dimensional spacetime. We show that intersections of $M5$ and $M2$ branes can instead lead to a large 4 dimensional spacetime. One dimensional intersections in 11D is related to (2,0) little strings (LST) on NS5 branes in type IIA. The gas regime of membranes in M-theory corresponds to the thermodynamics of LST obtained from holography. We propose a mechanism whereby LST living on the worldvolume of NS5 (M5)-branes wrapping a five dimensional torus, annihilate most efficiently in 3+1 dimensions leading to a large 3+1 dimensional spacetime. We also show that this picture is consistent with the gas approximation in M-theory.

Supersymmetry changing bubbles in string theory

We give examples of string compactifications to 4d Minkowski space with different amounts of supersymmetry that can be connected by spherical domain walls. The tension of these domain walls is tunably lower than the 4d Planck scale. The ``stringy'' description of these walls is known in terms of certain configurations of wrapped Dirichlet and NS branes. This construction allows us to connect a variety of vacua with 4d N=4,3,2,1 supersymmetry.

Rotating and orbiting strings in the near-horizon brane backgrounds

Using the Schwarzschild-type coordinates in stead of the global ones we reconstruct the classical rotating closed string solutions in the AdS*5 x S*5 backgrounds. They are explicitly described by the Jacobi elliptic and trigonometrical functions of worldsheet coordinates. We study the orbiting closed string configurations in the near-horizon geometries of Dp, NS1 and NS5 branes, and derive the energy and spin of them, whose relation takes a simple form for short strings. Specially in the D5 and NS5 backgrounds we have a linear relation that the energy of the point-like string is proportional to the spin, which is associated with the spectrum of strings in the pp-wave geometries obtained by taking a special Penrose limit on the D5 and NS5 backgrounds.

Penrose limits of branes and marginal intersecting branes

We construct the Penrose limit backgrounds in closed forms along the generic null geodesics for the near-horizon geometries of D1, D3, D5, NS1 and NS5 branes. The Penrose limit metrics of D1, D5 and NS1 have non-trivial dependence of the light-cone time coordinate, while those of D3 and NS5 have no its dependence. We study the Penrose limits on the marginal 1/4 supersymmetric configurations of standard intersecting branes, such as the NS–NS intersection of NS1 and NS5, the RR intersections of Dp and Dq over some spatial dimensions and the mix intersections of NS5 and Dp over (p−1)-dimensional spaces. They are classified into three types that correspond to the Penrose limits of D1, D3 and D5 backgrounds.

PP-Wave/CFT2Duality

We investigate the pp-wave limit of the AdS_3\times S^3\times K3 compactification of Type IIB string theory from the point of view of the dual Sym_N(K3) CFT. It is proposed that a fundamental string in this pp-wave geometry is dual to the c=6 effective string of the Sym_N(K3) CFT, with the string bits of the latter being composed of twist operators. The massive fundamental string oscillators correspond to certain twisted Virasoro generators in the effective string. It is shown that both the ground states and the genus expansion parameter (at least in the orbifold limit of the CFT) coincide. Surprisingly the latter scales like J^2/N rather than the J^4/N^2 which might have been expected. We demonstrate a leading-order agreement between the pp-wave and CFT particle spectra. For a degenerate special case (one NS 5-brane) an intriguing complete agreement is found.

Brane/flux annihilation and the string dual of a non-supersymmetric field theory

We consider the dynamics of p anti-D3 branes inside the Klebanov-Strassler geometry, the deformed conifold with M units of RR 3-form flux around the S^3. We find that for p<<M the system relaxes to a nonsupersymmetric NS 5-brane ``giant graviton'' configuration, which is classically stable, but quantum mechanically can tunnel to a nearby supersymmetric vacuum with M-p D3 branes. This decay mode is exponentially suppressed and proceeds via the nucleation of an NS 5-brane bubble wall. We propose a dual field theory interpretation of the decay as the transition between a nonsupersymmetric ``baryonic'' branch and a supersymmetric ``mesonic'' branch of the corresponding SU(2M-p)x SU(M-p) low energy gauge theory. The NS 5-brane tunneling process also provides a simple explanation of the geometric transition by which D3-branes can dissolve into 3-form flux.

Supergravity S-Branes

We construct supergravity solutions corresponding to space-like branes in string theory. Our approach is to apply the usual solution generating techniques to an appropriate time-dependent solution of the eleven dimensional vacuum Einstein equations. In this way all SDp-brane solutions are obtained, as well as the NS and M-theory space branes. Bound states of SDp/SD(p-2)- and SDp/SD(p-4)-branes are also constructed. Finally, we begin an investigation of the near-brane regions and singularity structure of these solutions.

Stable Non-Supersymmetric Supergravity Solutions from Deformations of the Maldacena-Nuñez Background

We study a deformation of the type IIB Maldacena-Nunez background which arises as the near-horizon limit of NS5 branes wrapped on a two-cycle. This background is dual to a "little string theory" compactified on a two-sphere, a theory which at low energies includes four-dimensional N = 1 super Yang-Mills theory. The deformation we study corresponds to a mass term for some of the scalar fields in this theory, and it breaks supersymmetry completely. In the language of seven-dimensional SO(4) gauged supergravity the deformation involves (at leading order) giving a VEV, depending only on the radial coordinate, to a particular scalar field. We explicitly construct the corresponding solution at leading order in the deformation, both in seven-dimensional and in ten-dimensional supergravity, and we verify that it completely breaks supersymmetry. Since the original background had a mass gap and we are performing a small deformation, the deformed background is guaranteed to be stable even though it is not supersymmetric.

Resolution of overlapping branes

We obtain singularity resolutions for various overlapping brane configurations, including those of two heterotic 5-branes, type II 5-branes or D4-branes. In these solutions, the “harmonic” function H for each brane component depends only on the associated four-dimensional relative transverse space. The resolution is achieved by replacing these transverse spaces with Eguchi–Hanson or Taub-NUT spaces, both of which admit a normalisable self-dual (or anti-self-dual) harmonic 2-form. Due to the manner in which the interaction terms for the form fields modify their Bianchi identities or equations of motion, these normalisable harmonic 2-forms provide regular sources for the branes. We also obtain resolved 5-branes and D4-branes wrapped on S1, which is fibred over the transverse Eguchi–Hanson or Taub-NUT spaces. The T-duality invariance of the NS–NS 5-brane is retained after the resolution. The resolved 5-branes and D4-branes provide regular supergravity duals of certain supersymmetric Yang–Mills theories in five and four dimensions.

D-branes in Massive IIA and Solitons in Chern-Simons Theory

We investigate D2-branes and D4-branes parallel to D8-branes. The low energy world volume theory on the branes is non-supersymmetric Chern-Simons theory. We identify the fundamental strings as the anyons of the 2+1 Chern-Simons theory and the D0-branes as solitons. The Chern-Simons theory with a boundary is modeled using NS 5-branes with ending D6-branes. The brane set-up provides for a graphical description of anomaly inflow. We also model the 4+1 Chern-Simons theory using branes and conjecture that D4-branes with a boundary describes a supersymmetric version of Kaplan's theory of chiral fermions.

(1+p)-dimensional open D(p−2) brane theories

The dynamics of a Dp brane can be described either by an open string ending on this brane or by an open D(p - 2) brane ending on the same Dp brane. The ends of the open string couple to a Dp brane worldvolume gauge field while the boundary of the open D(p - 2) brane couples to a (p - 2)-form worldvolume potential whose field strength is Poincare dual to that of the gauge field on the Dp-brane worldvolume. With this in mind, we find that the Poincare dual of the fixed rank-2 magnetic field used in defining a (1 + p)-dimensional noncommutative Yang-Mills (NCYM) gives precisely a near-critical electric field for the open D(p - 2) brane. We therefore find (1 + p)-dimensional open D(p - 2) brane theories along the same line as for obtaining noncommutative open string theories (NCOS), OM theory and open Dp brane theories (ODp) from NS5 brane. Similarly, the Poincare dual of the near-critical electric field used in defining a (1 + p)-dimensional NCOS gives a fixed magnetic-like field. This field along with the same bulk field scalings defines a (1 + p)-dimensional noncommutative field theory. In the same spirit, we can have various (1 + 5)-dimensional noncommutative field theories resulting from the existence of ODp if the description of open D(4 - p) brane ending on the NS5 brane is insisted.