Soo-Jong Rey

CRITICAL POINTS AND PHASE TRANSITIONS IN 5D COMPACTIFICATIONS OF M-THEORY

Abstract We study critical points of the BPS mass Z, the BPS string tension Zm, the black hole potential V and the gauged central charge potential P for M-theory compactified on Calabi-Yau three-folds. We first show that the stabilization equations for Z (determining the black hole entropy) take an extremely simple form in five dimensions as opposed to four dimensions. The stabilization equations for Zm are also very simple and determine the size of the infinite adS3throat of the string. The black hole potential in general exhibits two classes of critical points: supersymmetric critical points which coincide with those of the central charge and non-supersymmetric critical points. We then generalize the discussion to the entire extended Kahler cone encompassing topologically different but birationally equivalent Calabi-Yau three-folds that are connected via flop transitions. We examine behavior of the four potentials to probe the nature of these phase transitions. We find that V and P are continuous but not smooth across the flop transition, while Z and its first two derivatives, as well as Zm and its first derivative, are continuous. This in turn implies that supersymmetric stabilization of Z and Zm for a given configuration takes place in at most one point throughout the entire extended Kahler cone. The corresponding black holes (or string states) interpolate between different Calabi-Yau three-folds. At the boundaries of the extended Kahler cone we observe that electric states become massless and/or magnetic strings become tensionless.

Semirigid Construction of Topological Supergravities

We show how to construct topological N = 1 and 2 supergravity theories from appropriately constrained N = 3 and 4 ghost plus matter systems. In particular N = 4 susy is not needed to obtain the N = 1 topological theory. We give a description of the relevant supermoduli spaces which must be integrated to obtain the amplitudes of these theories, as well as explicit formulas for the ingredients entering the integrands, in particular the various supercurrents with their inhomogeneous terms.

M (atrix) theory on T5/Z2 orbifold and five-branes *

We study M(atrix) theory description of M theory compactified on T5/Z2 orbifold. In the large volume limit we show that M theory dynamics is described by N=8 supersymmetric USp(2N) M(atrix) quantum mechanics. Via zero-brane parton scattering, we show that each orbifold fixed point carries anomalous G-flux

Angular momentum of an electric charge and magnetically charged black hole

\oint [G/2 \pi]= - 1/2

Semiclassical gravity and invisible axions.

. To cancel the anomalous G-flux, we introduce twisted sector consisting of sixteen five-branes represented by fundamental representation hypermultiplets. In the small volume limit we show that M theory dynamics is described by by (5+1)-dimensional (8,0) supersymmetric USp(2N) chiral gauge theory. We point out that both perturbative and global gauge anomalies are cancelled by the sixteen fundamental representation hyper- multiplets in the twisted sector. We show that M(atrix) theory is capable of turning on spacetime background with the required sixteen five-branes out of zero-brane partons as bound-states. We determine six-dimensional spacetime spectrum from the M(atrix) theory for both untwisted and twisted sectors and find a complete agreement with the spectrum of (2,0) supergravity. We discuss M(atrix) theory description of compactification moduli space, symmetry enhance- ment thereof as well as further toroidal compactifications.

M(atrix) theory on orbifold and five-branes

We find the angular momentum L of a point particle with electric charge e held at a fixed position in the presence of a black hole with magnetic charge g. (For a point charge in the presence of an of ordinary magnetic monopole, it is known that L = eg). The angular momentum does depend on the separation distance between the particle and the black hole; however, L {yields} eg for a large separation. Implications for the cosmic censorship hypothesis, the quantum hairs and other physical situations are discussed.

A quenched c=1 critical matrix model

We show that charged Eguchi-Hanson instantons provide a concrete and calculable new source of intrinsic Peccei-Quinn symmetry breaking by quantum gravity. The size of this breaking is shown to depend sensitively on the short-distance details of a given theory, but is generically suppressed by fermion zero modes. Demanding that these gravitational effects not affect the axion solution to the strong CP problem, we find that at least two sets of quarks with differing Peccei-Quinn charges are required. In addition, these effects obviate the cosmological axion domain wall problem but leave unchanged problems associated with coherent axion oscillations.

Wilson-Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity

We study M(atrix) theory description of M theory compactified on T5/Z2 orbifold. In the large volume limit we show that M theory dynamics is described by N=8 supersymmetric USp(2N) M(atrix) quantum mechanics. Via zero-brane parton scattering, we show that each orbifold fixed point carries anomalous G-flux

Stringy domain walls and target-space modular invariance.

\oint [G/2 \pi]= - 1/2

Exactly soluble model of fractional statistics

. To cancel the anomalous G-flux, we introduce twisted sector consisting of sixteen five-branes represented by fundamental representation hypermultiplets. In the small volume limit we show that M theory dynamics is described by by (5+1)-dimensional (8,0) supersymmetric USp(2N) chiral gauge theory. We point out that both perturbative and global gauge anomalies are cancelled by the sixteen fundamental representation hyper- multiplets in the twisted sector. We show that M(atrix) theory is capable of turning on spacetime background with the required sixteen five-branes out of zero-brane partons as bound-states. We determine six-dimensional spacetime spectrum from the M(atrix) theory for both untwisted and twisted sectors and find a complete agreement with the spectrum of (2,0) supergravity. We discuss M(atrix) theory description of compactification moduli space, symmetry enhance- ment thereof as well as further toroidal compactifications.