99 research outputs found

### Two-Loop Superstrings III, Slice Independence and Absence of Ambiguities

The chiral superstring measure constructed in the earlier papers of this
series for general gravitino slices is examined in detail for slices supported
at two points x_\alpha. In this case, the invariance of the measure under
infinitesimal changes of gravitino slices established previously is
strengthened to its most powerful form: the measure is shown, point by point on
moduli space, to be locally and globally independent from the points x_\alpha,
as well as from the superghost insertion points p_a, q_\alpha introduced
earlier as computational devices. In particular, the measure is completely
unambiguous. The limit x_\alpha = q_\alpha is then well defined. It is of
special interest, since it elucidates some subtle issues in the construction of
the picture-changing operator Y(z) central to the BRST formalism. The formula
for the chiral superstring measure in this limit is derived explicitly.Comment: 20 pages, no figure

### Topics in Two-Loop Superstring Perturbation Theory

In this contribution to the Proceedings of the Conference on Analysis,
Complex Geometry, and Mathematical Physics, an expository overview of
superstring perturbation theory to two loop order is presented to an audience
of mathematicians and physicists. Recent results on perturbative supersymmetry
breaking effects in Heterotic string theory compactified on Z_2 \times Z_2
Calabi-Yau orbifolds, and the calculation of the two-loop vacuum energy in
these theories are discussed in detail, and the appearance of a new modular
identity with respect to Sp(4,Z)/Z_4 is reviewed.Comment: 27 pages, 5 figures, Dedicated to D.H. Phong on the occasion of his
60-th birthday; version 2 includes minor changes and added references in
section 1

### Exact M-Theory Solutions, Integrable Systems, and Superalgebras

In this paper, an overview is presented of the recent construction of fully
back-reacted half-BPS solutions in 11-dimensional supergravity which correspond
to near-horizon geometries of M2 branes ending on, or intersecting with, M5 and
M5$'$ branes along a self-dual string. These solutions have space-time manifold
${\rm AdS}_3 \times S^3 \times S^3$ warped over a Riemann surface $\Sigma$, and
are invariant under the exceptional Lie superalgebra $D(2,1;\gamma) \oplus
D(2,1;\gamma)$, where $\gamma$ is a real continuous parameter and $|\gamma|$
is governed by the ratio of the number of M5 and M5$'$ branes. The construction
proceeds by mapping the reduced BPS equations onto an integrable field theory
on $\Sigma$ which is of the Liouville sine-Gordon type. Families of regular
solutions are distinguished by the sign of $\gamma$, and include a
two-parameter Janus solution for $\gamma >0$, and self-dual strings on M5 as
well as asymptotically ${\rm AdS}_4/{\mathbb Z}_2$ solutions for $\gamma <0$.Comment: This paper is dedicated to Luc Vinet on the occasion of his 60-th
birthda

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