The Moduli Space and M(Atrix) Theory of 9d N=1 Backgrounds of M/String Theory

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 construct the M(atrix) theory for M theory on a Klein bottle (and the theories related to it), which is given by a 2 + 1 dimensional gauge theory with a varying gauge coupling compactified on a cylinder with specific boundary conditions. We also clarify the construction of the M(atrix) theory for backgrounds of rank 18, including the heterotic string on a circle.

Slowly rotating Einstein–Maxwell-dilaton black hole and some aspects of its thermodynamics

“…To do so one should use the equation of state (42) and express volume v in terms of mentioned above thermodynamic variables, but due to complicated form of the equation (42) it is impossible to perform in general case. It can be easily checked that the latter equation (52) gives rise to the conclusion that for the isobars above the critical one (P > P c ) the parameter κ T is always positive which means that the system is stable. Similarly one can talk about thermodynamic stability of the system for all the isotherms above the critical one (T > T c ).…”

“…This fact can be used for examination of possible extensions of AdS-CFT correspondence. It was also supposed that linear dilaton spacetime which appears as a near horizon limit of a dilatonic black hole might possess some holographic properties [52]. From the other side new black hole solutions which are not asymptotically flat nor of AdS-type (or dS-type) might be a good laboratory for application or testing of methods developed for the mentioned above types of black hole solutions.…”

The moduli space and M(atrix) theory of 9D Script N = 1 backgrounds of M/string theory

“…In toroidal compactifications of M theory, such dualities are related [43] to non-trivial dualities relating electric and magnetic fields in the M(atrix) theory gauge theories. We mentioned above that at the enhanced SU(2) symmetry points in space-time the M(atrix) theory is supposed to have a non-trivial enhanced SU(2) global symmetry (which can also be seen by viewing this theory as the theory of a D2-brane in a type I ′ background with an enhanced symmetry); the realization of this symmetry will be discussed in detail in [44]. More generally, there is a Z 2 duality symmetry relating the two sides of each graph in figures 1 and 2, which should map to a duality between two gauge theories in M(atrix) theory.…”

“…Unfortunately, so far we have only been able to find the M(atrix) description for the large radius region of the moduli space (as described above), and we could not yet find an independent (dual) description for the small radius region. It would be interesting to investigate this further [44]; it requires continuing the moduli space of backgrounds with O8 − planes beyond the point where the string coupling diverges at one of the orientifold planes, but without changing to the dual variables.…”

Semi-flatland

“…Nine dimensional CHL strings are defined by taking E8 × E8 heterotic strings and orbifolding by a Z2 action which shifts the ninth coordinate and interchanges the two E8 factors. For a recent study of the moduli space of nine dimensional theories with sixteen supercharges, see [78]. where (x, y, w) ∈ CP 2 1,2,1 and f 4 , g 8 are holomorphic sections of degree 4 and 8, respectively.…”