S. Kalyana Rama

Symplectic manifolds, coherent states, and semiclassical approximation

The symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds are described here. Using the two‐dimensional sphere (S2) and disc (D2) as illustrative cases, we write their path integral representations using coherent state techniques. These path integrals can be evaluated exactly by semiclassical methods, thus providing examples of the localization formula. Along the way, we also give a local coordinate description for a class of Grassmannians.

COSMOLOGICAL CONSTANT IN LOW ENERGY d = 4 STRING LEADS TO (STATIC SPHERICALLY SYMMETRIC) NAKED SINGULARITY

In the sigma model approach, the β-function equations for noncritical strings contain a term which acts like a tree level cosmological constant, Λ. We analyze the static, spherically symmetric solutions to these equations in d = 4 space-time, which will describe the gravitational field of a point star up to a distance r*, of the order of parsecs. We show that the curvature scalar seen by the strings is singular in these solutions if Λ ≠ 0. This singularity is naked. Requiring its absence up to a distance r* imposes the constraint in natural units. Thus if r* ≃ 1 Mpc then |Λ| < 10−114, and if r* extends all the way up to the edge of the universe (1028 cm) then |Λ| < 10−122 in natural units. From another point of view, our analysis implies that low energy d = 4 noncritical strings in the sigma model formulation lead to naked singularities.

Tachyon back-reaction on d=2 string black hole

Abstract We describe a static solution for d = 2 critical string theory including the tachyon T but with its potential V(T) set to zero. This solution thus incorporates a tachyon back-reaction and, when T = 0, reduces to the black hole solution. When T ≠ 0 we find that: (1) the Schwarzschild horizon of the above black hole splits into two, resembling Reissner-Nordstrom horizons, and (2) the curvature scalar develops new singularities at the horizons. We show that these features will persist even when V(T) is nonzero. We present a time-dependent extension of our static solution and discuss some possible methods for removing the above singularities.

COMMENTS ON WITTEN INVARIANTS OF THREE-MANIFOLDS FOR SU(2) AND Zm

The values of the Witten invariants, IW, of the lens space L(p,1) for SU(2) at level k are obtained for arbitrary p. A duality relation for IW when p and k are interchanged, valid for asymptotic k, is observed. A method for calculating IW for any group G is described. It is found that IW for Zm, even for m=2, distinguishes three-manifolds quite effectively.

Scenario for seeding a singularity in d = 2 string black hole with tachyon

Abstract The d = 2 string admits a black hole solution and also a singular solution when the tachyon back reaction is included. It is of importance to know if the former solution can evolve into the latter one. An explicit solution describing this process is difficult to obtain. We present here a scenario in which such an evolution is very likely to occur. In essence, it takes place when a derivative discontinuity is seeded in the dilaton field by an incident tachyon pulse. An application of this scenario to 1 + 1 dimensional toy models suggests that a black hole can evolve into a massive remnant, strengthening its candidacy for the end state of a black hole.