Note on M (Atrix) Theory In Seven Dimensions With Eight Supercharges

Physics Letters B, 1997

It has been proposed recently that, in the framework of M(atrix) theory, N = 8 supersymmetric U (N ) Yang-Mills theory in 1+1 dimensions gives rise to type IIA long string configurations. We point out that the quantum moduli space of SYM 1+1 gives rise to two quantum numbers, which fit very well into the M(atrix) theory. The two quantum numbers become familiar if one switches to a IIB picture, where they represent configurations of D-strings and fundamental strings. We argue that, due to the SL(2, Z) symmetry, of the IIB theory, such quantum numbers must represent configurations that are present also in the IIA framework.

2008

Compactifications of M-theory to two dimesnional space-time on (K3 × T 5)/Z2 and (K3 × K3 × S 1)/Z2 orientifolds are presented. These orientifolds provide examples of anomaly free chiral supergravity models in two dimensions with (8, 0) and (4, 0) supersymmetries. Anomaly free spectra at the enhanced symmetry points are also obtained. The results confirm the twisted sector contribution to the spectrum in the case of T 9 /Z2 discussed earlier. 1

Nuclear Physics B, 1999

We study the duality relationship between M-theory and heterotic string theory at the classical level, emphasising the transformations between the Kaluza-Klein reductions of these two theories on the K3 and T 3 manifolds. Particular attention is devoted to the corresponding structures of σ-model cosets and the correspondence between the p-brane charge lattices. We also present simple and detailed derivations of the global symmetries and coset structures of the toroidally-compactified heterotic theory in all dimensions D ≥ 3, making use of the formalism of solvable Lie algebras.

Nuclear Physics B, 1996

We study quantum effects in five dimensions in heterotic superstring theory compactified on K 3 × S 1 and analyze the conjecture that its dual effective theory is eleven-dimensional supergravity compactified on a Calabi-Yau threefold. This theory is also equivalent to type II superstring theory compactified on the same Calabi-Yau manifold, in an appropriate large volume limit. In this limit the conifold singularity disappears and is replaced by a singularity associated to enhanced gauge symmetries, as naïvely expected from the heterotic description. Furthermore, we exhibit the existence of additional massless states which appear in the strong coupling regime of the heterotic theory and are related to a different type of singular points on Calabi-Yau threefolds.

Nuclear Physics B, 1996

We study Z 2 -orbifolds of 11-dimensional M-theory on tori of various dimensions. The most interesting model (besides the known S 1 /Z 2 case) corresponds to T 5 /Z 2 , for which we argue that the resulting six-dimensional theory is equivalent to the type IIB string compactified on K3. Gravitational anomaly cancellation plays a crucial role in determining what states appear in the twisted sector. Most of the other models appear to break spacetime supersymmetry. We observe that M-theory tends to produce chiral compactifications on orbifolds, and that our results may provide an insight into the mechanism by which twisted-sector states arise in this hypothetical theory.

Physics Letters B, 1996

Compactifications of M-theory to two dimensional space-time on (K3 × T 5)/Z 2 and (K3 × K3 × S 1)/Z 2 orientifolds are presented. These orientifolds provide examples of anomaly free chiral supergravity models in two dimensions with (8, 0) and (4, 0) supersymmetries. Anomaly free spectra at the enhanced symmetry points are also obtained. The results confirm the twisted sector contribution to the spectrum in the case of T 9 /Z 2 discussed earlier.

Nuclear Physics B, 1997

Type II compactifications with varying string coupling can be described elegantly in F-theory/M-theory as compactifications on Umanifolds. Using a similar approach to describe Super Yang-Mills with a varying coupling constant, we argue that at generic points in Narain moduli space, the E 8 × E 8 Heterotic string compactified on T 2 is described in M(atrix) theory by N = 4 SYM in 3+1 dimensions with base S 1 × CP 1 and a holomorphically varying coupling constant. The CP 1 is best described as the base of an elliptic K3 whose fibre is the complexified coupling constant of the Super Yang-Mills theory leading to manifest U-duality. We also consider the cases of the Heterotic string on S 1 and T 3 . The twisted sector seems to (almost) naturally appear at precisely those points where enhancement of gauge symmetry is expected and need not be postulated. A unifying picture emerges in which the U-manifolds which describe type II orientifolds (dual to the Heterotic string) as M-or F-theory compactifications play a crucial role in Heterotic M(atrix) theory compactifications.

Nuclear Physics B, 2001

A massive version of T-duality in six dimensions is given, that maps the K3 compactification of Romans' theory onto the K3 compactification of Type IIB theory. This is done by performing a (standard) Kaluza-Klein reduction on six-dimensional massive Type IIA and a Scherk-Schwarz reduction on Type IIB, mapping both theories onto the same fivedimensional theory. We also comment shortly on the difficulties arising if one intends to construct a massive generalisation of the six-dimensional string-string duality.

Physics Letters B, 1997

We propose a construction of five-branes which fill both light-cone dimensions in Banks, Fischler, Shenker and Susskind's matrix model of M theory. We argue that they have the correct long-range fields and spectrum of excitations. We prove Dirac charge quantization with the membrane by showing that the five-brane induces a Berry phase in the membrane world-volume theory, with a familiar magnetic monopole form.

Nuclear Physics B, 1997

We study the M(atrix) theory which describes the E 8 × E 8 heterotic string compactified on S 1 , or equivalently M-theory compactified on an orbifold (S 1 /Z Z 2 ) × S 1 , in the presence of a Wilson line. We formulate the corresponding M(atrix) gauge theory, which lives on a dual orbifold S 1 × (S 1 /Z Z 2 ). Thirty-two real chiral fermions must be introduced to cancel gauge anomalies. In the absence of an E 8 × E 8 Wilson line, these fermions are symmetrically localized on the orbifold boundaries. Turning on the Wilson line moves these fermions into the interior of the orbifold. The M(atrix) theory action is uniquely determined by gauge and supersymmetry anomaly cancellation in 2+1 dimensions. The action consistently incorporates the massive I IA supergravity background into M(atrix) theory by explicitly breaking (2+1)-dimensional Poincaré invariance. The BPS excitations of M(atrix) theory are identified and compared to the heterotic string. We find that heterotic T-duality is realized as electric-magnetic S-duality in M(atrix) theory.

2007

Abstract: We discuss the moduli space of nine dimensional N = 1 supersymmetric compactifications of M theory / string theory with reduced rank (rank 10 or rank 2), exhibiting how all the different theories (including M theory compactified on a Klein bottle and on a Möbius strip, the Dabholkar-Park background, CHL strings and asymmetric orbifolds of type II strings on a circle) fit together, and what are the weakly coupled descriptions in different regions of the moduli space. We argue that there are two disconnected components in the moduli space of theories with rank 2. We analyze in detail the limits of the M theory compactifications on a Klein bottle and on a Möbius strip which naively give type IIA string theory with an uncharged orientifold 8-plane carrying discrete RR flux. In order to consistently describe these limits we conjecture that this orientifold non-perturbatively splits into a D8-brane and an orientifold plane of charge (−1) which sits at infinite coupling. We const...

Nuclear Physics B, 1997

We investigate compactifications of M-theory from 11 → 5 → 4 dimensions and discuss geometrical properties of 4-d moduli fields related to the structure of 5-d theory. We study supersymmetry breaking by compactification of the fifth dimension and find that an universal superpotential is generated for the axion-dilaton superfield S. The resulting theory has a vacuum with < S >= 1, zero cosmological constant and a gravitino mass depending on the fifth radius as m 3/2 ∼ R −2 5 /M P l. We discuss phenomenological aspects of this scenario, mainly the string unification and the decompactification problem.

Physics Letters B, 1997

We construct M-theory curves associated with brane configurations of SU( N ), SO(N) and Sp(2 N) 5D supersymmetric gauge theories compactified on a circle. From the curves we can account for all the existing different SU( N) field theories with Nf 5 2 N. This is the correct bound for N 2 3. We remark on the exceptional case SU(2). The bounds obtained for SO(N) and Sp(2N) are Nf< N -4 and Nf< 2 N + 4, respectively. 0 1997 Elsevier Science B.V. 0370.2693/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved.

Physics Letters B, 1997

We demonstrate the precise numerical correspondence between long range scattering of supergravitons and membranes in supergravity in the infinite momentum frame and in M(atrix)-theory, both in 11 dimensions and for toroidal compactifications. We also identify wrapped membranes in terms of topological invariants of the vector bundles associated to the field theory description of compactified M(atrix)-theory. We use these results to

1999

We present a class of N=1 supersymmetric models of particle physics, derived directly from heterotic M-theory, that contain three families of chiral quarks and leptons coupled to the gauge group $SU(3)_C\times SU(2)_{L}\times U(1)_{Y}$. These models are a fundamental form of ``brane-world&#x27;&#x27; theories, with an observable and hidden sector each confined, after compactification on a Calabi-Yau threefold, to a BPS threebrane separated by a five-dimensional bulk space with size of the order of the intermediate scale. The requirement of three families, coupled to the fundamental conditions of anomaly freedom and supersymmetry, constrains these models to contain additional fivebranes wrapped around holomorphic curves in the Calabi-Yau threefold. These fivebranes ``live&#x27;&#x27; in the bulk space and represent new, non-perturbative aspects of these particle physics vacua. We discuss, in detail, the relevant mathematical structure of a class of torus-fibered Calabi-Yau threefolds...