arXiv subjects

Spenta R. Wadia

Publications and source records attributed to Spenta R. Wadia.

69 records · Page 4Linked to original sources

arXiv1995

Discrete State Moduli of String Theory from c=1 Matrix Model

We propose a new formulation of the space-time interpretation of the $c=1$ matrix model. Our formulation uses the well-known leg-pole factor that relates the matrix model amplitudes to that of the 2-dimensional string theory, but includes fluctuations around the fermi vacuum on {\sl both sides} of the inverted harmonic oscillator potential of the double-scaled model, even when the fluctuations are small and confined entirely within the asymptotes in the phase plane. We argue that including fluctuations on both sides of the potential is essential for a consistent interpretation of the leg-pole transformed theory as a theory of space-time gravity. We reproduce the known results for the string theory tree level scattering amplitudes for flat space and linear dilaton background as a special case. We show that the generic case corresponds to more general space-time backgrounds. In particular, we identify the parameter corresponding to background metric perturbation in string theory (black hole mass) in terms of the matrix model variables. Possible implications of our work for a consistent nonperturbative definition of string theory as well as for quantized gravity and black-hole physics are discussed.

hep-th↗

arXiv1995

A VIEW OF 2-DIM. STRING THEORY AND BLACK HOLES

We present a brief overview of 2-dim. string theory and its connection to the theory of non-relativistic fermions in one dimension. We emphasize (i) the role of $W_\infty$ algebra and (ii) the modelling of some aspects of 2-dim. black hole physics using the phase space representation of the fermi fluid.

hep-th↗

arXiv1994

$W_\infty$ Algebra and Geometric Formulation of QCD$_2$

We review the gauge invariant formulation of 2-dim. QCD. We show that the non-linear gauge invariant phase space is the coset $W_\infty/W_{+\infty}\times W_{-\infty}$ ,which is specified by the $N=\infty$ master-field of this model. The meson fields correspond to the local coordinates of the coset. We comment on the stringy collective coordinates of the solitons (baryons) in this model.

hep-th↗

arXiv1994

Leading Large N Modification of QCD_2 on a Cylinder by Dynamical Fermions

We consider 2-dimensional QCD on a cylinder, where space is a circle. We find the ground state of the system in case of massless quarks in a $1/N$ expansion. We find that coupling to fermions nontrivially modifies the large $N$ saddle point of the gauge theory due to the phenomenon of `decompactification' of eigenvalues of the gauge field. We calculate the vacuum energy and the vacuum expectation value of the Wilson loop operator both of which show a nontrivial dependence on the number of quarks flavours at the leading order in $1/N$.

hep-th↗

arXiv1994

Universal Cellular Automata and Class 4

Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long transients). These properties of Class 4 CA's has led to the conjecture that Class 4 rules are Universal Turing machines i.e. they are bases for computational universality. We describe an embedding of a ``small'' universal Turing machine due to Minsky, into a cellular automaton rule-table. This produces a collection of $(k=18,r=1)$ cellular automata, all of which are computationally universal. However, we observe that these rules are distributed amongst the various Wolfram classes. More precisely, we show that the identification of the Wolfram class depends crucially on the set of initial conditions used to simulate the given CA. This work, among others, indicates that a description of complex systems and information dynamics may need a new framework for non-equilibrium statistical mechanics.

cond-mat↗

arXiv1994

String Field Theory of Two Dimensional QCD on a Cylinder: A Realization of W-infinity Current Algebra

We consider 2-dimensional QCD on a cylinder, where space is a circle of length $L$. We formulate the theory in terms of gauge-invariant gluon operators and multiple-winding meson (open string) operators. The meson bilocal operators satisfy a $W_\infty$ current algebra. The gluon sector (closed strings) contains purely quantum mechanical degrees of freedom. The description of this sector in terms of non-relativistic fermions leads to a $W_\infty$ algebra. The spectrum of excitations of the full theory is therefore organized according to two different algebras: a wedge subalgebra of $W_\infty$ current algebra in the meson sector and a wedge subalgebra of $W_\infty$ algebra in the glueball sector. In the large $N$ limit the theory becomes semiclassical and an effective description for the gluon degrees of freedom can be obtained. We have solved the effective theory of the gluons in the small $L$ limit. We get a glueball spectrum which coincides with the `discrete states' of the (Euclidean) $c=1$ string theory. We remark on the implications of these results for (a) QCD at finite temperature and (b) string theory.

hep-th↗

arXiv1994

String Field Theory of Two Dimensional QCD: A Realization of W-infinity Algebra

We consider the formulation of two dimensional QCD in terms of gauge invariant bilocal operators (string field) which satisfy a $W_\infty$ algebra. In analogy with our work on the $c=1$ string field theory we derive an action and associated constraints for the bilocal field using the method of coadjoint orbits. The $1/N$ perturbation theory around a classical solution that corresponds to the filled Dirac sea leads to the 'tHooft equation for meson fluctuations. It is shown that the spectrum of mesons, which are the higher string modes, transform as a representation of the wedge subalgebra $W_{\infty+} \otimes W_{\infty-}$. We briefly discuss the baryon as a stringy solitonic configuration and its characterization in terms of $W_\infty$ algebra.

hep-th↗

arXiv1993

$W_\infty$ coherent states and path-integral derivation of bosonization of non-relativistic fermions in one dimension

We complete the proof of bosonization of noninteracting nonrelativistic fermions in one space dimension by deriving the bosonized action using $W_\infty$ coherent states in the fermion path-integral. This action was earlier derived by us using the method of coadjoint orbits. We also discuss the classical limit of the bosonized theory and indicate the precise nature of the truncation of the full theory that leads to the collective field theory.

hep-th↗

arXiv1993

Non-Perturbative 2-Dimensional String Theory

We review some aspects of the non-perturbative formulation of 2-dim. string theory in terms of non-relativistic fermions. We derive the bosonization using $W_\infty$ coherent states in the path-integral formulation. We discuss the classical limit and indicate the precise nature of the truncation of the full theory that leads to collective field theory. As applications we briefly discuss classical solutions reponsible for stringy non-perturbative effects and the 2-dim. black-hole.

hep-th↗

arXiv1992

A Time-Dependent Classical Solution of C=1 String Field Theory and Non-Perturbative Effects

We describe a real-time classical solution of $c=1$ string field theory written in terms of the phase space density, $u(p,q,t)$, of the equivalent fermion theory. The solution corresponds to tunnelling of a single fermion above the filled fermi sea and leads to amplitudes that go as $\exp(- C/ \gst)$. We discuss how one can use this technique to describe non-perturbative effects in the Marinari-Parisi model. We also discuss implications of this type of solution for the two-dimensional black hole.

hep-th↗

arXiv1992

Non-relativistic Fermions, Coadjoint Orbits of \winf\ and String Field Theory at $c=1$

We apply the method of coadjoint orbits of \winf-algebra to the problem of non-relativistic fermions in one dimension. This leads to a geometric formulation of the quantum theory in terms of the quantum phase space distribution of the fermi fluid. The action has an infinite series expansion in the string coupling, which to leading order reduces to the previously discussed geometric action for the classical fermi fluid based on the group $w_\infty$ of area-preserving diffeomorphisms. We briefly discuss the strong coupling limit of the string theory which, unlike the weak coupling regime, does not seem to admit of a two dimensional space-time picture. Our methods are equally applicable to interacting fermions in one dimension.

hep-th↗

arXiv1992

Classical Fermi Fluid and Geometric Action for $c=1$

We formulate the $c=1$ matrix model as a quantum fluid and discuss its classical limit in detail, emphasizing the $\hbar$ corrections. We view the fermi fluid profiles as elements of \winf-coadjoint orbit and write down a geometric action for the classical phase space. In the specific representation of fluid profiles as `strings' the action is written in a four-dimensional form in terms of gauge fields built out of the embedding of the `string' in the phase plane. We show that the collective field action can be derived from the above action provided one restricts to quadratic fluid profiles and ignores the dynamics of their `turning points'.

hep-th↗

arXiv1991

$W$-Infinity Ward Identities and Correlation Functions in the $C=1$ Matrix Model

We explore consequences of $W$-infinity symmetry in the fermionic field theory of the $c=1$ matrix model. We derive exact Ward identities relating correlation functions of the bilocal operator. These identities can be expressed as equations satisfied by the effective action of a {\it three} dimensional theory and contain non-perturbative information about the model. We use these identities to calculate the two point function of the bilocal operator in the double scaling limit. We extract the operator whose two point correlator has a {\it single} pole at an (imaginary) integer value of the energy. We then rewrite the \winf~ charges in terms of operators in the matrix model and use this derive constraints satisfied by the partition function of the matrix model with a general time dependent potential.

hep-th↗

arXiv1991

Bosonization of Nonrelativistic Fermions and W-infinity Algebra

We discuss the bosonization of non-relativistic fermions in one space dimension in terms of bilocal operators which are naturally related to the generators of $W$-infinity algebra. The resulting system is analogous to the problem of a spin in a magnetic field for the group $W$-infinity. The new dynamical variables turn out to be $W$-infinity group elements valued in the coset $W$-infinity/$H$ where $H$ is a Cartan subalgebra. A classical action with an $H$ gauge invariance is presented. This action is three-dimensional. It turns out to be similiar to the action that describes the colour degrees of freedom of a Yang-Mills particle in a fixed external field. We also discuss the relation of this action with the one we recently arrived at in the Euclidean continuation of the theory using different coordinates.

hep-th↗

arXiv1991

Gauge Theory Formulation of the $c=1$ Matrix Model: Symmetries and Discrete States

We present a non-relativistic fermionic field theory in 2-dimensions coupled to external gauge fields. The singlet sector of the $c=1$ matrix model corresponds to a specific external gauge field. The gauge theory is one-dimensional (time) and the space coordinate is treated as a group index. The generators of the gauge algebra are polynomials in the single particle momentum and position operators and they form the group $W^{(+)}_{1+\infty}$. There are corresponding Ward identities and residual gauge transformations that leave the external gauge fields invariant. We discuss the realization of these residual symmetries in the Minkowski time theory and conclude that the symmetries generated by the polynomial basis are not realized. We motivate and present an analytic continuation of the model which realises the group of residual symmetries. We consider the classical limit of this theory and make the correspondence with the discrete states of the $c=1$ (Euclidean time) Liouville theory. We explain the appearance of the $SL(2)$ structure in $W^{(+)}_{1+\infty}$. We also present all the Euclidean classical solutions and the classical action in the classical phase space. A possible relation of this theory to the $N=2$ string theory and also self-dual Einstein gravity in 4-dimensions is pointed out.

hep-th↗