23 research outputs found
Conformal Supergravity in Twistor-String Theory
Conformal supergravity arises in presently known formulations of
twistor-string theory either via closed strings or via gauge-singlet open
strings. We explore this sector of twistor-string theory, relating the relevant
string modes to the particles and fields of conformal supergravity. We also use
the twistor-string theory to compute some tree level scattering amplitudes with
supergravitons, and compare to expectations from conformal supergravity. Since
the supergravitons interact with the same coupling constant as the Yang-Mills
fields, conformal supergravity states will contribute to loop amplitudes of
Yang-Mills gluons in these theories. Those loop amplitudes will therefore not
coincide with the loop amplitudes of pure super Yang-Mills theory.Comment: 43 pages harvmac tex, added footnote to introductio
Central extensions of current groups in two dimensions
In this paper we generalize some of these results for loop algebras and
groups as well as for the Virasoro algebra to the two-dimensional case. We
define and study a class of infinite dimensional complex Lie groups which are
central extensions of the group of smooth maps from a two dimensional
orientable surface without boundary to a simple complex Lie group G. These
extensions naturally correspond to complex curves. The kernel of such an
extension is the Jacobian of the curve. The study of the coadjoint action shows
that its orbits are labelled by moduli of holomorphic principal G-bundles over
the curve and can be described in the language of partial differential
equations. In genus one it is also possible to describe the orbits as conjugacy
classes of the twisted loop group, which leads to consideration of difference
equations for holomorphic functions. This gives rise to a hope that the
described groups should possess a counterpart of the rich representation theory
that has been developed for loop groups. We also define a two-dimensional
analogue of the Virasoro algebra associated with a complex curve. In genus one,
a study of a complex analogue of Hill's operator yields a description of
invariants of the coadjoint action of this Lie algebra. The answer turns out to
be the same as in dimension one: the invariants coincide with those for the
extended algebra of currents in sl(2).Comment: 17 page
Supersymmetric Gauge Theories in Twistor Space
We construct a twistor space action for N=4 super Yang-Mills theory and show
that it is equivalent to its four dimensional spacetime counterpart at the
level of perturbation theory. We compare our partition function to the original
twistor-string proposal, showing that although our theory is closely related to
string theory, it is free from conformal supergravity. We also provide twistor
actions for gauge theories with N<4 supersymmetry, and show how matter
multiplets may be coupled to the gauge sector.Comment: 23 pages, no figure
Modular Invariance and Uniqueness of Conformal Characters
We show that the conformal characters of various rational models of
W-algebras can be already uniquely determined if one merely knows the central
charge and the conformal dimensions. As a side result we develop several tools
for studying representations of SL(2,Z) on spaces of modular functions. These
methods, applied here only to certain rational conformal field theories, may be
useful for the analysis of many others.Comment: 21 pages (AMS TeX), BONN-TH-94-16, MPI-94-6
Quantum Group as Semi-infinite Cohomology
We obtain the quantum group as semi-infinite cohomology of the
Virasoro algebra with values in a tensor product of two braided vertex operator
algebras with complementary central charges . Each braided VOA is
constructed from the free Fock space realization of the Virasoro algebra with
an additional q-deformed harmonic oscillator degree of freedom. The braided VOA
structure arises from the theory of local systems over configuration spaces and
it yields an associative algebra structure on the cohomology. We explicitly
provide the four cohomology classes that serve as the generators of
and verify their relations. We also discuss the possible extensions of our
construction and its connection to the Liouville model and minimal string
theory.Comment: 50 pages, 7 figures, minor revisions, typos corrected, Communications
in Mathematical Physics, in pres
Limits on the monopole magnetic field from measurements of the electric dipole moments of atoms, molecules and the neutron
A radial magnetic field can induce a time invariance violating electric
dipole moment (EDM) in quantum systems. The EDMs of the Tl, Cs, Xe and Hg atoms
and the neutron that are produced by such a field are estimated. The
contributions of such a field to the constants, of the T,P-odd
interactions and are also estimated for the TlF, HgF and YbF molecules (where
() is the electron (nuclear) spin and is the molecular
axis). The best limit on the contact monopole field can be obtained from the
measured value of the Tl EDM. The possibility of such a field being produced
from polarization of the vacuum of electrically charged magnetic monopoles
(dyons) by a Coulomb field is discussed, as well as the limit on these dyons.
An alternative mechanism involves chromomagnetic and chromoelectric fields in
QCD.Comment: Uses RevTex, 16 pages, 4 postscript figures. An explanation of why
there is no orbital contribution to the EDM has been added, and the
presentation has been improved in genera
BRST Quantization of String Theory in AdS(3)
We study the BRST quantization of bosonic and NSR strings propagating in
AdS(3) x N backgrounds. The no-ghost theorem is proved using the
Frenkel-Garland-Zuckerman method. Regular and spectrally-flowed representations
of affine SL(2,R) appear on an equal footing. Possible generalizations to
related curved backgrounds are discussed.Comment: JHEP style, 23 pages; v2:minor changes and references added; v3:
typos corrected, version to appear in JHEP; v4: one reference adde
Itsy bitsy topological field theory
We construct an elementary, combinatorial kind of topological quantum field
theory, based on curves, surfaces, and orientations. The construction derives
from contact invariants in sutured Floer homology and is essentially an
elaboration of a TQFT defined by Honda--Kazez--Matic. This topological field
theory stores information in binary format on a surface and has "digital"
creation and annihilation operators, giving a toy-model embodiment of "it from
bit".Comment: 54 pages, 35 figures. Minor edits, extra figures adde
In search of the QCD-Gravity correspondence
Quantum Chromodynamics (QCD) is the fundamental theory of strong
interactions. It describes the behavior of quarks and gluons which are the
smallest known constituents of nuclear matter. The difficulties in solving the
theory at low energies in the strongly interacting, non-perturbative regime
have left unanswered many important questions in QCD, such as the nature of
confinement or the mechanism of hadronization. In these lectures oriented
towards the students we introduce two classes of dualities that attempt to
reproduce many of the features of QCD, while making the treatment at strong
coupling more tractable: (1) the AdS/CFT correspondence between a specific
class of string theories and a conformal field theory and (2) an effective
low-energy theory of QCD dual to classical QCD on a curved conformal
gravitational background. The hope is that by applying these dualities to the
evaluation of various properties of the strongly-interacting matter produced in
heavy ion collisions one can understand how QCD behaves at strong coupling. We
give an outline of the applications, with emphasis on two transport
coefficients of QCD matter -- shear and bulk viscosities.Comment: 31 pages, 7 figures; Lectures delivered by D. Kharzeev at the
International QGP Winter School, Jaipur, India, February 1-3, 200
The Dipion Mass Spectrum In e+e- Annihilation and tau Decay: A Dynamical (rho0, omega, phi) Mixing Approach
We readdress the problem of finding a simultaneous description of the pion
form factor data in e+e- annihilations and in tau decays. For this purpose, we
work in the framework of the Hidden Local Symmetry (HLS) Lagrangian and modify
the vector meson mass term by including the pion and kaon loop contributions.
This leads us to define the physical rho, omega and phi fields as linear
combinations of their ideal partners, with coefficients being meromorphic
functions of s, the square of the 4--momentum flowing into the vector meson
lines. This allows us to define a dynamical, i.e. s-dependent, vector meson
mixing scheme. The model is overconstrained by extending the framework in order
to include the description of all meson radiative (V P gamma and P gamma gamma
couplings) and leptonic (Ve+e- couplings) decays and also the isospin breaking
(omega/ phi --> pi+ pi-) decay modes. The model provides a simultaneous,
consistent and good description of the e+e- and tau dipion spectra. The
expression for pion form factor in the latter case is derived from those in the
former case by switching off the isospin breaking effects specific to e+e- and
switching on those for tau decays. Besides, the model also provides a good
account of all decay modes of the form V P gamma, Pgamma gamma as well as the
isospin breaking decay modes. It leads us to propose new reference values for
the rho^0 --> e+ e- and omega --> pi+ pi- partial widths which are part of our
description of the pion form factor. Other topics (phi --> K anti K, the rho
meson mass and width parameters) are briefly discussed. Therefore, we confirm
the 3.3 sigma discrepancy between the theoretical estimate of a_mu based on
e+e- and its direct BNL measurement.Comment: 71 pages, 8 figures. Accepted by EPJ C. Version 3: correct minor
typos, minor changes spread out into the text. Extension of Sections 12.2 and
12.3.5 and introduction of the new Appendix