75 research outputs found

### Behavior of tachyon in string cosmology based on gauged WZW model

We investigate a string theoretic cosmological model in the context of the
gauged Wess-Zumino-Witten model. Our model is based on a product of non-compact
coset space and a spectator flat space; $[SL(2,R)/U(1)]_k \times {\bf R}^2$. We
extend the formerly studied semiclassical consideration with infinite Kac-Moody
level $k$ to a finite one. In this case, the tachyon field appears in the
effective action, and we solve the Einstein equation to determine the behavior
of tachyon as a function of time. We find that tachyon field dominates over
dilaton field in early times. In particular, we consider the energy conditions
of the matter fields consisting of the dilaton and the tachyon which affect the
initial singularity. We find that not only the strong energy but also the null
energy condition is violated.Comment: 10 figure

### Knizhnik-Zamolodchikov-type equations for gauged WZNW models

We study correlation functions of coset constructions by utilizing the method
of gauge dressing. As an example we apply this method to the minimal models and
to the Witten 2D black hole. We exhibit a striking similarity between the
latter and the gravitational dressing. In particular, we look for logarithmic
operators in the 2D black hole.Comment: 24 pages, latex, no figures. More discussion of logarithmic operators
was adde

### Marginal Deformations of WZNW and Coset Models from O(d,d) Transformation

We show that O(2,2) transformation of SU(2) WZNW model gives rise to marginal
deformation of this model by the operator $\int d^2 z J(z)\bar J(\bar z)$ where
$J$, $\bar J$ are U(1) currents in the Cartan subalgebra. Generalization of
this result to other WZNW theories is discussed. We also consider O(3,3)
transformation of the product of an SU(2) WZNW model and a gauged SU(2) WZNW
model. The three parameter set of models obtained after the transformation is
shown to be the result of first deforming the product of two SU(2) WZNW
theories by marginal operators of the form $\sum_{i,j=1}^2 C_{ij} J_i \bar
J_j$, and then gauging an appropriate U(1) subgroup of the theory. Our analysis
leads to a general conjecture that O(d,d) transformation of any WZNW model
corresponds to marginal deformation of the WZNW theory by combination of
appropriate left and right moving currents belonging to the Cartan subalgebra;
and O(d,d) transformation of a gauged WZNW model can be identified to the
gauged version of such marginally deformed WZNW models.Comment: 26 pages, phyzzx.tex, TIFR-TH-92-6

### Subtleties in QCD theory in Two Dimensions

It is shown that in a formulation of Yang-Mills theory in two dimensions in
terms of A=if^{-1}\pa f, \bar A=i\bar f\bpa\bar f^{-1} with $f(z,\bar z)$,
$\bar f(z,\bar z)\in[SU(N_C)]^c$ the complexification of $SU(N_C)$ , reveals
certain subtleties. ``Physical" massive color singlet states seem to exist.
When coupled to $N_F$ quarks the coupling constant is renormalized in such a
way that it vanishes for the pure Yang- Mills case. This renders the above
states massless and unphysical. In the abelian case, on the other hand, the
known results of the Schwinger model are reproduced with no need of such a
renormalization.
The massless $QCD_2$ theory is analyzed in similar terms and peculiar massive
states appear, with a mass of $e_c\sqrt {N_F \over 2\pi}$.Comment: 21 page

### Two Dimensional QCD coupled to Adjoint Matter and String Theory

We study $2d$ QCD coupled to fermions in the adjoint representation of the
gauge group $SU(N)$ at large $N$, and its relation to string theory. It is
shown that the model undergoes a deconfinement transition at a finite
temperature (analogous to the Hagedorn transition in string theory), with
certain winding modes in the Euclidean time direction turning tachyonic at high
temperature. The theory is supersymmetric for a certain ratio of quark mass and
gauge coupling. For other values of that ratio, supersymmetry is softly broken.
The spectrum of bound states contains an infinite number of approximately
linear Regge trajectories, approaching at large mass $M$, $\alpha^\prime
M^2=\sum_i i l_i$ $(l_i\in{\bf Z_+})$. Thus, the theory exhibits an
exponentially growing density of bosonic and fermionic states at high energy.
We discuss these results in light of string expectations.Comment: harvmac, 19 pages, EFI-93-3

### c=1 String Theory as a Topological G/G Model

The physical states on the free field Fock space of the {SL(2,R)\over
SL(2,R) model at any level are computed. Using a similarity transformation on
$Q_{BRST}$, the cohomology of the latter is mapped into a direct sum of simpler
cohomologies. We show a one to one correspondence between the states of the
$k=-1$ model and those of the $c=1$ string model. A full equivalence between
the {SL(2,R)\over SL(2,R) and {SL(2,R)\over U(1) models at the level of
their Fock space cohomologies is found.Comment: 19

### On the twisted G/H topological models

The twisted G/H models are constructed as twisted supersymmetric gauged WZW
models. We analyze the case of $G=SU(N)$, $H=SU(N_1)\times ...\times
SU(N_n)\times U(1)^r$ with $rank\ G =\ rank\ H$, and discuss possible
generalizations. We introduce a non-abelian bosonization of the $(1,0)$ ghost
system in the adjoint of $H$ and in G/H. By computing chiral anomalies in the
latter picture we write the quantum action as a decoupled sum of ``matter",
gauge and ghost sectors. The action is also derived in the unbosonized version.
We invoke a free field parametrization and extract the space of physical states
by computing the cohomology of $Q$ , the sum of the BRST gauge-fixing charge
and the twisted supersymmetry charge. For a given $G$ we briefly discuss the
relation between the various G/H models corresponding to different choices of
$H$. The choice $H=G$ corresponds to the topological G/G theory.Comment: 27 page

### Knot invariants from rational conformal field theories

A framework for studying knot and link invariants from any rational conformal
field theory is developed. In particular, minimal models, superconformal models
and $W_N$ models are studied. The invariants are related to the invariants
obtained from the Wess-Zumino models associated with the coset representations
of these models. Possible Chern-Simons representation of these models is also
indicated. This generalises the earlier work on knot and link invariants from
Chern-Simons theories.Comment: 18pages+6 figures (available on request through email

### The Spectrum of Sl(2, R)/U(1) Black Hole Conformal Field Theory

We study string theory in the background of a two-dimensional black hole
which is described by an $SL(2, R)/U(1)$ coset conformal field theory. We
determine the spectrum of this conformal field theory using supersymmetric
quantum mechanics and give an explicit form of the vertex operators in terms of
the Jacobi functions. We also discuss the applicability of SUSY quantum
mechanics techniques to non-linear $\sigma$-models.Comment: 21 page

### Cosmological String Backgrounds from Gauged WZW Models

We discuss the four-dimensional target-space interpretation of bosonic
strings based on gauged WZW models, in particular of those based on the
non-compact coset space $SL(2,{\bf R})\times SO(1,1)^2 /SO(1,1)$. We show that
these theories lead, apart from the recently broadly discussed black-hole type
of backgrounds, to cosmological string backgrounds, such as an expanding
Universe. Which of the two cases is realized depends on the sign of the level
of the corresponding Kac-Moody algebra. We discuss various aspects of these new
cosmological string backgrounds.Comment: 11 page

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