Three-form Field Research Articles

The maximal [formula omitted] supergravities

The general seven-dimensional maximal supergravity is presented. Its universal Lagrangian is described in terms of an embedding tensor which can be characterized group-theoretically. The theory generically combines vector, two-form and three-form tensor fields that transform into each other under an intricate set of non-Abelian gauge transformations. The embedding tensor encodes the proper distribution of the degrees of freedom among these fields. In addition to the kinetic terms the vector and tensor fields contribute to the Lagrangian with a unique gauge-invariant Chern–Simons term. This new formulation encompasses all possible gaugings. Examples include the sphere reductions of M-theory and of the type IIA/IIB theories with gauge groups SO ( 5 ) , CSO ( 4 , 1 ) , and SO ( 4 ) , respectively.

Standardlike models as type IIB flux vacua

We construct new semirealistic type IIB flux vacua on ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ orientifolds with three- and four-standard model families and up to three units of quantized flux. The open string sector is comprised of magnetized D-branes and is T-dual to supersymmetric intersecting D6-brane constructions. The standard model sector contains magnetized D9-branes with negative D3-brane charge contribution. There are large classes of such models and we present explicit constructions for representative ones. In addition to models with one and two units of quantized flux, we also construct the first three- and four-family standard-like models with supersymmetric fluxes, i.e. comprising three units of quantized flux. Supergravity fluxes are due to the self-dual Neveu-Schwarz-Neveu-Schwarz and Ramond-Ramond three-form field strength and they fix the toroidal complex structure moduli and the dilaton. The supersymmetry conditions for the D-brane sector fix in some models all three toroidal K\"ahler moduli. We also provide examples where toroidal K\"ahler moduli are fixed by strong gauge dynamics on the ``hidden sector'' D7-brane. Most of the models possess Higgs doublet pairs with Yukawa couplings that can generate masses for quarks and leptons. The models have (mainly right-) chiral exotics.

On the formulation of D = 11 supergravity and the composite nature of its three-form gauge field

The underlying gauge group structure of the D = 11 Cremmer–Julia–Scherk supergravity becomes manifest when its three-form field A 3 is expressed through a set of one-form gauge fields, B 1 a 1 a 2 , B 1 a 1 ⋯ a 5 , η 1 α , and E a , ψ α . These are associated with the generators of the elements of a family of enlarged supersymmetry algebras E ˜ ( 528 | 32 + 32 ) ( s ) parametrized by a real number s. We study in detail the composite structure of A 3 extending previous results by D’Auria and Fré, stress the equivalence of the above problem to the trivialization of a standard supersymmetry algebra E ( 11 | 32 ) cohomology four-cocycle on the enlarged E ˜ ( 528 | 32 + 32 ) ( s ) superalgebras, and discuss its possible dynamical consequences. To this aim we consider the properties of the first order supergravity action with a composite A 3 field and find the set of extra gauge symmetries that guarantee that the field theoretical degrees of freedom of the theory remain the same as with a fundamental A 3. The extra gauge symmetries are also present in the so–called rheonomic treatment of the first order D = 11 supergravity action when A 3 is composite. Our considerations on the composite structure of A 3 provide one more application of the idea that there exists an extended superspace coordinates/fields correspondence. They also suggest that there is a possible embedding of D = 11 supergravity into a theory defined on the enlarged superspace Σ ˜ ( 528 | 32 + 32 ) ( s ) .

Open membranes, ribbons, and deformed Schild strings

We analyze open membranes immersed in a magnetic three-form field strength C. While cylindrical membranes in the absence of C behave like tensionless strings, when the C flux is present the strings polarize into thin membrane ribbons, locally orthogonal to the momentum density, thus providing the strings with an effective tension. The effective dynamics of the ribbons can be described by a simple deformation of the Schild action for null strings. Interactions become non-local due to the polarization, and lead to a deformation of the string field theory, whereby string vertices receive a phase factor proportional to the volume swept out by the ribbons. In a particular limit, this reduces to the non-commutative loop space found previously.

On the underlying gauge group structure of [formula omitted] supergravity

The underlying gauge group structure of D=11 supergravity is revisited. It may be described by a one-parametric family of Lie supergroups Σ˜(s)×⊃SO(1,10), s≠0. The family of superalgebras E˜(s) associated to Σ˜(s) is given by a family of extensions of the M-algebra {Pa,Qα,Zab,Za1⋯a5} by an additional fermionic central charge Qα′. The Chevalley–Eilenberg four-cocycle ω4∼Πα∧Πβ∧Πa∧ΠbΓabαβ on the standard D=11 supersymmetry algebra may be trivialized on E˜(s), and this implies that the three-form field A3 of D=11 supergravity may be expressed as a composite of the Σ˜(s) one-form gauge fields ea, ψα, Bab, Ba1⋯a5 and ηα. Two superalgebras of E˜(s) recover the two earlier D'Auria and Fré decompositions of A3. Another member of E˜(s) allows for a simpler composite structure for A3 that does not involve the Ba1⋯a5 field. Σ˜(s) is a deformation of Σ˜(0), which is singularized by having an enhanced Sp(32) (rather than just SO(1,10)) automorphism symmetry and by being an expansion of OSp(1|32).

Exchange of orientifold two-planes in M theory

We propose an M-theory lift picture of the exchange among type IIA orientifold two-planes. This consists in wrapping a M5-brane on a three-cycle in the transverse space of the M-theory orientifold plane OM2. A flux quantization condition for the three-form self-dual field strength, on the worldvolume of the M5-brane is computed. This condition establishes the value which explains the relative charge between two different OM2-planes. Also, we find that the exchange of the four types of orientifold two-planes in string theory, has a common picture in M-theory. Moreover, we find that the assignment of the extra charge is fixed by cohomology and by the flux quantization of the field strength G in M-theory. We conclude that cohomology is sufficient to describe some orientifold properties in M-theory, that at string theory level, only K-theory is able to explain.

Solvable models of strings in homogeneous plane-wave backgrounds

We solve closed string theory in all regular homogeneous plane-wave backgrounds with homogeneous NS three-form field strength and a dilaton. The parameters of the model are constant symmetric and anti-symmetric matrices k ij and f ij associated with the metric, and a constant anti-symmetric matrix h ij associated with the NS field strength. In the light-cone gauge the rotation parameters f ij have a natural interpretation as a constant magnetic field. This is a generalisation of the standard Landau problem with oscillator energies now being non-trivial functions of the parameters f ij and k ij . We develop a general procedure for solving linear but non-diagonal equations for string coordinates, and determine the corresponding oscillator frequencies, the light-cone Hamiltonian and level matching condition. We investigate the resulting string spectrum in detail in the four-dimensional case and compare the results with previously studied examples. Throughout we will find that the presence of the rotation parameter f ij can lead to certain unusual and unexpected features of the string spectrum like new massless states at non-zero string levels, stabilisation of otherwise unstable (tachyonic) modes, and discrete but not positive definite string oscillator spectra.

Free tensor multiplets and strings in spontaneously broken six-dimensional (2,0) theory

We first review the representations of the six-dimensional (2,0) superalgebra on a free tensor multiplet and on a free string. We then construct a supersymmetric Lagrangian describing a free tensor multiplet. (It also includes a decoupled anti self-dual part of the three-form field strength.) This field theory is then rewritten in variables appropriate for analyzing a situation where the R-symmetry is spontaneously broken by the vacuum expectation values of the scalar moduli fields. Finally, we construct a supersymmetric and kappa-symmetric action for a free string.

Neveu-Schwarz 5-branes in type-IIA supergravity and gravitational anomalies

We construct a gravitational-anomaly-free effective action for the coupled system of type-IIA $D=10$ dynamical supergravity interacting with a NS5-brane. The NS5-brane is considered as elementary in that the associated current is a $\ensuremath{\delta}$ function supported on its world volume. Our approach is based on a Chern kernel which encodes the singularities of the three-form field strength near the brane in an SO(4)-invariant way and provides a solution for its Bianchi identity in terms of a two-form potential. A dimensional reduction of the recently constructed anomaly-free effective action for an elementary M5-brane in $D=11$ is seen to reproduce our ten-dimensional action. The Chern-kernel approach provides in particular a concrete realization of the anomaly cancellation mechanism envisaged by Witten.

THE d = 6, (2, 0)-TENSOR MULTIPLET COUPLED TO SELF-DUAL STRINGS

We show that the central charges that group theory allows in the (2, 0)-supersymmetry translations algebra arise from a string and a three-brane by commuting two supercharges. We show that the net force between two such parallel strings vanishes. We show that all the coupling constants are fixed numbers, due to supersymmetry, and self-duality of the three-form field strength. We obtain a charge quantization for the self-dual field strength, and show that when compactifying on a two-torus, it reduces to the usual quantization condition of N = 4 SYM with gauge group SU(2), and with coupling constant and theta angle given by the τ-parameter of the two-torus, provided that we pick that chiral theory which corresponds to a theta function with zero characteristics, as expected on manifolds of this form.

An [formula omitted] supersymmetric G2-invariant flow in M-theory

It was found that deformation of S 7 gives rise to renormalization group (RG) flow from N=8 , SO(8)-invariant UV fixed point to N=1 , G 2-invariant IR fixed point in four-dimensional gauged N=8 supergravity. Also BPS supersymmetric domain wall configuration interpolated between these two critical points. In this paper, we use the G 2-invariant RG flow equations for both scalar fields and domain wall amplitude and apply them to the nonlinear metric ansatz developed by de Wit, Nicolai and Warner some time ago. We carry out the M-theory lift of the G 2-invariant RG flow through a combinatoric use of the four-dimensional RG flow equations and eleven-dimensional Einstein–Maxwell equations. The nontrivial r (that is the coordinate transverse to the domain wall)-dependence of vacuum expectation values makes the Einstein–Maxwell equations consistent not only at the critical points but also along the supersymmetric RG flow connecting two critical points. By applying an ansatz for an eleven-dimensional three-form gauge field with varying scalars, we discover an exact solution to the eleven-dimensional Einstein–Maxwell equations corresponding to the M-theory lift of the G 2-invariant RG flow.

Type IIB supergravity compactified on a Calabi-Yau manifold with H-fluxes

We discuss the compactification of type IIB supergravity on a Calabi-Yau manifold in the presence of both RR and NS fluxes for the three-form fields. We obtain the classical potential both by direct compactification and by using the techniques of N=2 gauged supergravity in four-dimensions. We briefly discuss the properties of such potential and compare the result with previous derivations.

Bogomol’nyi-Prasad-Sommerfield solitons in M5-brane worldvolume theory with a constant three-form field

We study BPS solutions for a self-dual string and a neutral string in M5-brane worldvolume theory with constant three-form field. We further generalize such solitons to superpose with a calibrated surface. We also study a traveling wave on a calibrated surface in the constant three-form field background.

Open branes in space–time non-commutative little string theory

We conjecture the existence of two new non-gravitational six-dimensional string theories, defined as the decoupling limit of NS5-branes in the background of near-critical electrical two- and three-form RR fields. These theories are space-time non-commutative Little String Theories with open branes. The theory with (2,0) supersymmetry has an open membrane in the spectrum and reduces to OM theory at low energies. The theory with (1,1) supersymmetry has an open string in the spectrum and reduces to 5+1 dimensional NCOS theory for weak NCOS coupling and low energies. The theories are shown to be T-dual with the open membrane being T-dual to the open string. The theories therefore provide a connection between 5+1 dimensional NCOS theory and OM theory. We study the supergravity duals of these theories and we consider a chain of dualities that shows how the T-duality between the two theories is connected with the S-duality between 4+1 dimensional NCOS theory and OM theory.

OM theory in diverse dimensions

Open string theories can be decoupled from closed strings and gravity by scaling to the critical electric field. We propose dual descriptions for the strong coupling limit of these NCOS (Non-Commutative Open String) theories in six or fewer spacetime dimensions. In particular, we conjecture that the five-dimensionsal NCOS theory at strong coupling, is a theory of light Open Membranes (OM), decoupled from gravity, on an M5-brane with a near-critical three-form field strength. The relation of OM theory to NCOS theories resembles that of M theory to Type II closed string theories. In two dimensions we conjecture that supersymmetric U($n$) gauge theory with a unit of electric flux is dual to the NCOS theory with string coupling $1 \over n$. A construction based on NS5-branes leads to new theories in six dimensions generalising the little string theory. A web of dualities relates all the above theories when they are compactified on tori.

Nonlinear instantons from supersymmetric p-branes

Supersymmetric configurations of type II D-branes with nonzero gauge field strengths in general supersymmetric backgrounds with nonzero B fields are analyzed using the kappa-symmetric worldvolume action. It is found in dimension four or greater that the usual instanton equation for the gauge field obtains a nonlinear deformation. The deformation is parameterized by the topological data of the B-field, the background geometry and the cycle wrapped by the brane. In the appropriate dimensions, limits and settings these equations reduce to deformed instanton equations recently found in the context of noncommutative geometry as well as those following from Lagrangians based on Bott-Chern forms. We further consider instantons comprised of M5-branes wrapping a Calabi-Yau space with non-vanishing three-form field strengths. It is shown that the instanton equations for the three-form are related to the Kodaira-Spencer equations.

ALTERNATIVE FORMULATION FOR DUALITY-SYMMETRIC 11-DIMENSIONAL SUPERGRAVITY COUPLED TO SUPER M-5-BRANE

We present an alternative formulation of duality-symmetric 11-dimensional supergravity with both three-form and six-form gauge fields. Instead of the recently-proposed scalar auxiliary field, we use a simpler Lagrangian with a non-propagating auxiliary multiplier tensor field with eight-indices. We also complete the superspace formulation in a duality-symmetric manner. An alternative super M-5-brane action coupled to this 11-dimensional background is also presented. This formulation bypasses the usual obstruction for an invariant Lagrangian for a self-dual three-form field strength, by allowing the self-duality only as a solution for field equations, but not as a necessary condition.

SL(4, R) generating symmetry in five-dimensional gravity coupled to dilaton and three-form

We give an explicit formulation of the three-dimensional SL(4,R)/SO(2,2) σ -model representing the five-dimensional Einstein gravity coupled to the dilaton and the three-form field for spacetimes with two commuting Killing vector fields. New matrix representation is obtained which is similar to one found earlier in the four-dimensional Einstein–Maxwell–Dilaton–Axion (EMDA) theory. The SL(4, R) symmetry joins a variety of 5 D solutions of different physical types including strings, 0-branes, KK monopoles etc. interpreting them as duals to the four-dimensional Kerr metric translated along the fifth coordinate. The symmetry transformations are used to construct new rotating strings and composite (0–1)-branes endowed with a NUT parameter.

SUPEREMBEDDINGS, NONLINEAR SUPERSYMMETRY AND FIVE-BRANES

We examine general properties of superembeddings, i.e. embeddings of supermanifolds into supermanifolds. The connection between an embedding procedure and the method of nonlinearly realized supersymmetry is clarified, and we demonstrate how the latter arises as a special case of the former. As an illustration, the super-5-brane in seven dimensions, containing a self-dual three-form world volume field strength, is formulated in both languages, and provides an example of a model where the embedding condition does not suffice to put the theory on-shell.

Twisted bundle on quantum torus and BPS states in matrix theory

Following the recent work of Connes, Douglas and Schwarz, we study the M(atrix) model compactified on a torus with a background of the three-form field. This model is given by a super Yang-Mills theory on a quantum torus. To consider twisted gauge field configurations, we construct twisted U( n) bundles on the quantum torus as a deformation of its classical counterpart. By properly taking into account membranes winding around the light-cone direction, we derive from the M(atrix) model the BPS spectrum which respects the full SL(2, Z)×SL(2, Z) U-duality in M theory.