M2-brane Theory Research Articles

QUANTUM DESCRIPTION FOR THE DECAY OF NSNS BRANE–ANTIBRANE SYSTEMS

The stringy description for the instabilities in the RR charged [Formula: see text] pairs is now well understood in terms of the open string tachyon condensation. The quantum interpretation presumably via the stringy description for the instabilities in the NSNS-charged [Formula: see text] and [Formula: see text] pairs in IIA/IIB theories, however, has not been fully established yet. This would be partly because of the absence (for the [Formula: see text] case) or our relatively poor understanding (for the [Formula: see text] case) of their world-volume (gauge theory) dynamics. In the present work, using the well-known quantum description for instabilities in the RR-charged [Formula: see text] systems and in the M-theory brane–antibrane systems and invoking appropriate string dualities, the stringy nature of the instabilities in the NSNS-charged [Formula: see text] and [Formula: see text] systems both at strong and at weak couplings has been uncovered. For the annihilations to string vacua, the quantum, stringy interpretations are simple extensions of Sen's conjecture for those in RR-charged brane–antibrane systems.

Bubbling AdS space and 1/2 BPS geometries

We consider all 1/2 BPS excitations of $AdS \times S$ configurations in both type IIB string theory and M-theory. In the dual field theories these excitations are described by free fermions. Configurations which are dual to arbitrary droplets of free fermions in phase space correspond to smooth geometries with no horizons. In fact, the ten dimensional geometry contains a special two dimensional plane which can be identified with the phase space of the free fermion system. The topology of the resulting geometries depends only on the topology of the collection of droplets on this plane. These solutions also give a very explicit realization of the geometric transitions between branes and fluxes. We also describe all 1/2 BPS excitations of plane wave geometries. The problem of finding the explicit geometries is reduced to solving a Laplace (or Toda) equation with simple boundary conditions. We present a large class of explicit solutions. In addition, we are led to a rather general class of $AdS_5$ compactifications of M-theory preserving ${\cal N} =2$ superconformal symmetry. We also find smooth geometries that correspond to various vacua of the maximally supersymmetric mass-deformed M2 brane theory. Finally, we present a smooth 1/2 BPS solution of seven dimensional gauged supergravity corresponding to a condensate of one of the charged scalars.

New Phases of Near-Extremal Branes on a Circle

We study the phases of near-extremal branes on a circle, by which we mean near-extremal branes of string theory and M-theory with a circle in their transverse space. We find a map that takes any static and neutral Kaluza-Klein black hole, i.e. any static and neutral black hole on Minkowski-space times a circle d × S1, and map it to a corresponding solution for a near-extremal brane on a circle. The map is derived using first a combined boost and U-duality transformation on the Kaluza-Klein black hole, transforming it to a solution for a non-extremal brane on a circle. The resulting solution for a near-extremal brane on a circle is then obtained by taking a certain near-extremal limit. As a consequence of the map, we can transform the neutral non-uniform black string branch into a new non-uniform phase of near-extremal branes on a circle. Furthermore, we use recently obtained analytical results on small black holes in Minkowski-space times a circle to get new information about the localized phase of near-extremal branes on a circle. This gives in turn predictions for the thermal behavior of the non-gravitational theories dual to these near-extremal branes. In particular, we give predictions for the thermodynamics of supersymmetric Yang-Mills theories on a circle, and we find a new stable phase of (2,0) Little String Theory in the canonical ensemble for temperatures above its Hagedorn temperature.

The off-shell M5-brane and non-perturbative gauge theory

M5-branes wrapping a holomorphic curve in a Calabi–Yau manifold can be used to construct four-dimensional N = 1 gauge theories. In this paper we will consider M5-brane configurations corresponding to N = 2 theories broken to N = 1 by a superpotential for the adjoint scalar field. These M5-brane configurations can be obtained by lifting suitable intersecting brane configurations in type IIA, or equivalently by T-dualizing IIB configurations with branes and/or fluxes. We will show that turning on non-trivial expectation values for the glueball superfields corresponds to non-holomorphic deformations of the M5-brane. We compute the superpotential and show it agrees with that computed by Dijkgraaf and Vafa. Several aspects of the gauge theory, such as the appearance of non-holomorphic one-forms with integer periods on the Seiberg–Witten curve, have a natural interpretation from the M5-brane point of view. We also explain the interpretation of the superpotential in terms of the twisted ( 2 , 0 ) theory living on the fivebrane.

The Domain Walls of Gauged Maximal Supergravities and their M-theory Origin

We consider gauged maximal supergravities with CSO(p,q,r) gauge groups and their relation to the branes of string and M-theory. The gauge groups are characterised by n mass parameters, where n is the transverse dimension of the brane. We give the scalar potentials and construct the corresponding domain wall solutions. In addition, we show the higher-dimensional origin of the domain walls in terms of (distributions of) branes. We put particular emphasis on the CSO(p,q,r) gauged supergravities in D=9 and D=8, which are related to the D7-brane and D6-brane, respectively. In these cases, twisted and group manifold reductions are shown to play a crucial role. We also discuss salient features of the corresponding brane distributions.

Dimensional reductions of M-theory S-branes to string theory S-branes

We study both the direct and the double-dimensional reduction of space-like branes of M-theory and point out some peculiarities in the process unlike their time-like counterpart. In particular, we show how starting from SM2 and SM5-brane solutions we can obtain SD2 and SNS5-brane as well as SNS1 and SD4-brane solutions of string theory by direct and double-dimensional reductions, respectively. In the former case we need to use delocalized SM-brane solutions, whereas in the latter case we need to use anisotropic SM-brane solutions in the directions which are compactified.

Topological charges for branes in M-theory

We propose a simple form for the superalgebra of M2 and M5-brane probes in arbitrary supersymmetric backgrounds of 11D supergravity, extending previous results in the literature. In particular, we identify the topological charges in the algebras and find BPS bounds for the energies. The charges are given by the integral over a brane's spatial worldvolume of a certain closed form built out of the Killing spinors and background fields. The existence of such closed forms for arbitrary supersymmetric backgrounds generalises the existence of calibration forms for special holonomy manifolds.

Counting BPS states of the M5-brane

An on-shell model for the supersymmetric index counting multiplicities of BPS states of the M5-brane theory is reviewed. In particular we explicitly study the tensionless Little String states appearing at intersections in a bound state of $N$ 5-branes wrapped on a six-manifold with product topology $M_4\times T^2$.

World-volume description of M2-branes ending on an M5-brane and holography

We consider world-volume description of M2-branes ending on an M5-brane. The system can be described either as a solitonic solution of the M5-brane field equations or in terms of an effective string propagating in 6 dimensions. We show that the zeroth order scalar scattering amplitudes behave similarly in both pictures. The soliton solution appears to have a horizon-like throat region. Due to the underlying geometric structure of the M5-brane theory, modes propagating near the horizon are subject to a large red-shift. This allows one to define a decoupling limit and implies a holographic duality between two theories which do not contain dynamical gravity.

Brane world supersymmetry breaking

In brane world models of nature, supersymmetry breaking is often isolated on a distant brane in a higher dimensional space. The form of the K\ahler potential in generic string and M-theory brane world backgrounds is shown to give rise to tree-level nonuniversal squark and slepton masses. This results from the exchange of bulk supergravity fields and warping of the internal geometry. This is contrary to the notion that bulk locality gives rise to a sequestered no-scale form of the K\ahler potential with vanishing tree-level masses and solves the supersymmetric flavor problem. As a result, a radiatively generated anomaly mediated superpartner spectrum is not a generic outcome of these theories.

A membrane action for WM2 / OM theory

Through direct examination of the effect of the OM limit on the M2-brane worldvolume action, we derive a membrane action for OM theory, and more generally, for the eleven-dimensional M-theoretic construct known as Galilean or Wrapped M2-brane (WM2) theory, which contains OM theory as a special class of states. In the static gauge, the action in question implies a discrete spectrum for the closed membrane of WM2 theory, which under double dimensional reduction is shown to reproduce the known NCOS/Wound closed string spectrum. We examine as well open membranes ending on each of the three types of M5-branes in WM2 theory (OM theory arising from the ‘longitudinal’ type), and show that the ‘fully transverse’ fivebrane is tensionless. As a prelude to the membrane, we also study the case of the string, where we likewise obtain a reparametrization-invariant action, and make contact with previous work.

Integrable reductions of Spin(7)- and G2-invariant self-dual Yang–Mills equations and gravity

There is remarkable relation between self-dual Yang–Mills and self-dual Einstein gravity in four Euclidean dimensions. Motivated by this we investigate the Spin(7)- and G 2-invariant self-dual Yang–Mills equations in eight and seven Euclidean dimensions and search for their possible analogs in gravitational theories. The reduction of the self-dual Yang–Mills equations to one dimension results into systems of first order differential equations. In particular, the Spin(7)-invariant case gives rise to a 7-dimensional system which is completely integrable. The different solutions are classified in terms of algebraic curves and are characterized by the genus of the associated Riemann surfaces. Remarkably, this system arises also in the construction of solutions in gauged supergravities that have an interpretation as continuous distributions of branes in string and M-theory. For the G 2-invariant case we perform two distinct reductions, both giving rise to 6-dimensional systems. The first reduction, which is a complex generalization of the 3-dimensional Euler spinning top system, preserves an SU(2)× SU(2)× Z 2 symmetry and is fully integrable in the particular case where an extra U(1) symmetry exists. The second reduction we employ, generalizes the Halphen system familiar from the dynamics of monopoles. Finally, we analyze massive generalizations and present solitonic solutions interpolating between different degenerate vacua.

Five-branes in heterotic brane-world theories

The effective action for five-dimensional heterotic M-theory in the presence of five-branes is systematically derived from Horava-Witten theory coupled to an M5-brane world-volume theory. This leads to a five-dimensional N=1 gauged supergravity theory on S^1/Z_2 coupled to four-dimensional N=1 theories residing on the two orbifold fixed planes and an additional bulk three-brane. We analyse the properties of this action, particularly the four-dimensional effective theory associated with the domain-wall vacuum state. The moduli Kahler potential and the gauge-kinetic functions are determined along with the explicit relations between four-dimensional superfields and five-dimensional component fields.

Discrete Torsion and Branes in M-theory

Discrete Torsion and Branes in M-theory

Supersymmetric index of the M-theory 5-brane and little string theory

We propose a six-dimensional framework to calculate the supersymmetric index of M-theory 5-branes wrapped on a six-manifold with product topology $M_4\times T^2$, where $M_4$ is a holomorphic 4-cycle in a Calabi-Yau three-fold. This is obtained by zero-modes counting of the self-dual tensor contribution plus ``little'' string states and correctly reproduces the known results which can be obtained by shrinking or blowing the $T^2$ volume parameter. We also extract the geometric moduli space of the multi M5-brane system and infer the generic structure of the supersymmetric index for more general geometries.

Dirac branes, characteristic currents and anomaly cancellations in 5-branes

The aim of this note is to discuss, in a somewhat informal language, the cancellation of anomalies (in topologically trivial space-time) for 5-branes using as “building blocks”: i) a generalization to p-branes of the Dirac strings of monopoles (Dirac branes) and a refinement of this idea involving a geometric regularization of Dirac branes, leading to the formalism of “characteristic currents” ii) the PST formalism. As an example of the potentiality of the developed framework we discuss in some detail the anomaly cancellation in the D = 10 effective theory of heterotic string and 5-brane coupled to supergravity, where the anomaly inflow is automatically generated. Some remarks are also made on a similar approach to the problem of anomaly cancellation in the effective theory of M5-brane coupled to D=11 supergravity, developed in collaboration with M. Tonin, where however still as open problem remains a Dirac anomaly.

The M5-brane andnon-commutative loop space

We investigate, in a certain decoupling limit, the effect of having aconstant C-field on the M-theory 5-brane using an open-membraneprobe. We define an open-membrane metric for the 5-brane thatremains non-degenerate in the limit. The canonical quantization of theopen-membrane boundary leads to a non-commutative loop space which isa functional analogue of the non-commutative geometry that occurs forD-branes.

The M5-brane andnon-commutative open strings

The M-theory origin of non-commutative open-string theory is examined byinvestigating the M-theory 5-brane at near critical field strength. Inparticular, it is argued that the open-membrane metric providesthe appropriate moduli when calculating the duality relations between Mand II non-commutative theories.

Discrete torsion and branes in M-theory from mathematical viewpoint

We study orbifold group actions on locally defined fields upon M-theory branes in a three-form C-fields background. We derive some constraints from the consistency of the orbifold group actions. We show the possibility of the existence of M-theory discrete torsion for the fields on the worldvolume and discuss its features.

Branes from Unstable Systems of Branes

We discuss various aspects of the description of branes as topological solitons in unstable brane systems of higher dimensions. We first describe a classification of all the possible realisations of branes of M and type II theories as topological solitons of a brane-antibrane system. We then present a description of type IIB NS-NS p-branes in terms of topological solitons in systems of spacetime-filling NS9, anti-NS9 pairs and discuss the implications of these constructions in the description of BPS and non-BPS states in the strongly coupled Heterotic SO(32) theory. We finally present briefly the construction of a conjectured spacetime-filling non-BPS M10-brane, starting point for a brane descent construction of the branes of M-theory.