115 research outputs found
Bosonization of non-relativistic fermions on a circle: Tomonaga's problem revisited
We use the recently developed tools for an exact bosonization of a finite
number of non-relativistic fermions to discuss the classic Tomonaga
problem. In the case of noninteracting fermions, the bosonized hamiltonian
naturally splits into an O piece and an O piece. We show that in the
large-N and low-energy limit, the O piece in the hamiltonian describes a
massless relativistic boson, while the O piece gives rise to cubic
self-interactions of the boson. At finite and high energies, the low-energy
effective description breaks down and the exact bosonized hamiltonian must be
used. We also comment on the connection between the Tomonaga problem and pure
Yang-Mills theory on a cylinder. In the dual context of baby universes and
multiple black holes in string theory, we point out that the O piece in
our bosonized hamiltonian provides a simple understanding of the origin of two
different kinds of nonperturbative O corrections to the black hole
partition function.Comment: latex, 28 pages, 5 epsf figure
A Time-Dependent Classical Solution of C=1 String Field Theory and Non-Perturbative Effects
We describe a real-time classical solution of string field theory
written in terms of the phase space density, , 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.Comment: 23
Wave Propagation in Stringy Black Hole
We further study the nonperturbative formulation of two-dimensional black
holes. We find a nonlinear differential equation satisfied by the tachyon in
the black hole background. We show that singularities in the tachyon field
configurations are always associated with divergent semiclassical expansions
and are absent in the exact theory. We also discuss how the Euclidian black
hole emerges from an analytically continued fermion theory that corresponds to
the right side up harmonic oscillator potential.Comment: 23p, TIFR-TH-93/05; (v3) tex error correcte
Stringy Quantum Effects in 2-Dimensional Black-Hole
We discuss the classical 2-dim. black-hole in the framework of the
non-perturbative formulation (in terms of non-relativistic fermions) of c=1
string field theory. We identify an off-shell operator whose classical equation
of motion is that of tachyon in the classical graviton-dilaton black-hole
background. The black-hole `singularity' is identified with the fermi surface
in the phase space of a single fermion, and as such is a consequence of the
semi-classical approximation. An exact treatment reveals that stringy quantum
effects wash away the classical singularity.Comment: 17p, TIFR/TH/92-63; (v3) tex error correcte
Classical Fermi Fluid and Geometric Action for
We formulate the matrix model as a quantum fluid and discuss its
classical limit in detail, emphasizing the 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'.Comment: 31 pages. (Revised version
Non-relativistic Fermions, Coadjoint Orbits of \winf\ and String Field Theory at
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 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.Comment: 22 page
Probing Type I' String Theory Using D0 and D4-Branes
We analyse the velocity-dependent potentials seen by D0 and D4-brane probes
moving in Type I' background for head-on scattering off the fixed planes. We
find that at short distances (compared to string length) the D0-brane probe has
a nontrivial moduli space metric, in agreement with the prediction of Type I'
matrix model; however, at large distances it is modified by massive open
strings to a flat metric, which is consistent with the spacetime equations of
motion of Type I' theory. We discuss the implication of this result for the
matrix model proposal for M-theory. We also find that the nontrivial metric at
short distances in the moduli space action of the D0-brane probe is reflected
in the coefficient of the higher dimensional v^4 term in the D4-brane probe
action.Comment: 12 pages, latex. References added and some typos correcte
Renormalization group flows in a Lifshitz-like four fermi model
We study renormalization group flows in the Lifshitz-like -flavour four
fermi model discussed in 0905.2928. In the large- limit, a nontrivial flow
occurs in only one of all possible marginal couplings and one relevant
coupling, which provides the scale for Lorentz invariance violations. We
discuss in detail the phase diagram and RG flows in the space of couplings,
which includes the Lifshitz fixed point, the free field fixed point and a new
fixed point characterized by scaling and a violation of Lorentz
invariance, which cannot be tuned away by adjusting a parameter. In the broken
symmetry phase, the model flows from the Lifshitz-like fixed point in the
ultraviolet to this new fixed point in the infrared. However, in a modified
version of the present model, which has an effective ultraviolet cut-off much
smaller than the Lorentz invariance violating scale, the infrared behaviour is
governed by an approximately Lorentz invariant theory, similar to the low
energy limit of the usual relativistic NambuJona-Lasinio model. Such a
modified model could be realized by a supersymmetric version of the present
model.Comment: 30 pages, 2 figure
Gauge Theory Formulation of the 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 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 .
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 (Euclidean time)
Liouville theory. We explain the appearance of the structure in
. 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 string theory and also self-dual Einstein gravity in
4-dimensions is pointed out.Comment: 35 page
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