16,714 research outputs found

### Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model

We study the IIB matrix model, which is conjectured to be a nonperturbative
definition of superstring theory, by introducing an integer deformation
parameter `nu' which couples to the imaginary part of the effective action
induced by fermions. The deformed IIB matrix model continues to be well-defined
for arbitrary `nu', and it preserves gauge invariance, Lorentz invariance, and
the cluster property. We study the model at `nu' = infinity using a
saddle-point analysis, and show that ten-dimensional Lorentz invariance is
spontaneously broken at least down to an eight-dimensional one. We argue that
it is likely that the remaining eight-dimensional Lorentz invariance is further
broken, which can be checked by integrating over the saddle-point
configurations using standard Monte Carlo simulation.Comment: 12 pages, latex, no figures, references added, version to appear in
JHE

### Ginsparg-Wilson Fermions in Odd Dimensions

The Ginsparg-Wilson relation, if written in a suitable form, can be used as a
condition for lattice Dirac operators of massless fermions also in odd
dimensions. The fermion action with such a Dirac operator is invariant under a
generalized parity transformation, which reduces to the ordinary parity
transformation in the (naive) continuum limit. The fermion measure, however,
transforms non-trivially under the generalized parity transformation, and hence
the parity anomaly arises solely from the fermion measure. The analogy to the
lattice construction of chiral gauge theories in even dimensions is clarified
by considering a dimensional reduction. We also propose a natural definition of
a lattice Chern-Simons term, which is consistent with odd dimensional
Ginsparg-Wilson fermions.Comment: 15 pages, no figures, final version published in JHE

### Applications of the overlap formalism to super Yang-Mills theories

We show that the idea to use the overlap formalism to formulate 4D N=1 super
Yang-Mills theory on the lattice without fine-tuning can be applied to 3D N=1
case as well. Another application we propose is a regularization of the IIB
matrix model, which is large N reduced model of 10D N=1 super Yang-Mills
theory.Comment: 3 pages, LaTeX with espcrc2.sty. Talk presented at Lattice97,
Edinburgh, 22-26 July 1997, to appear in Nucl. Phys. B (Proc.Suppl.

### Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals

We advocate a method to improve systematically the self-consistent harmonic
approximation (or the Gaussian approximation), which has been employed
extensively in condensed matter physics and statistical mechanics. We
demonstrate the {\em convergence} of the method in a model obtained from
dimensional reduction of SU($N$) Yang-Mills theory in $D$ dimensions. Explicit
calculations have been carried out up to the 7th order in the large-N limit,
and we do observe a clear convergence to Monte Carlo results. For $D \gtrsim
10$ the convergence is already achieved at the 3rd order, which suggests that
the method is particularly useful for studying the IIB matrix model, a
conjectured nonperturbative definition of type IIB superstring theory.Comment: LaTeX, 4 pages, 5 figures; title slightly changed, explanations added
(16 pages, 14 figures), final version published in JHE

### On the Quantum Geometry of String Theory

The IKKT or IIB matrix model has been proposed as a non-perturbative
definition of type IIB superstring theories. It has the attractive feature that
space--time appears dynamically. It is possible that lower dimensional
universes dominate the theory, therefore providing a dynamical solution to the
reduction of space--time dimensionality. We summarize recent works that show
the central role of the phase of the fermion determinant in the possible
realization of such a scenario.Comment: 3 pages, 2 figures, Lattice2001(surfaces

### Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings

We study the properties of the space-time that emerges dynamically from the
matrix model for type IIB superstrings in ten dimensions. We calculate the free
energy and the extent of space-time using the Gaussian expansion method up to
the third order. Unlike previous works, we study the SO(d) symmetric vacua with
all possible values of d within the range $2 \le d \le 7$, and observe clear
indication of plateaus in the parameter space of the Gaussian action, which is
crucial for the results to be reliable. The obtained results indeed exhibit
systematic dependence on d, which turns out to be surprisingly similar to what
was observed recently in an analogous work on the six-dimensional version of
the model. In particular, we find the following properties: i) the extent in
the shrunken directions is given by a constant, which does not depend on d; ii)
the ten-dimensional volume of the Euclidean space-time is given by a constant,
which does not depend on d except for d = 2; iii) The free energy takes the
minimum value at d = 3. Intuitive understanding of these results is given by
using the low-energy effective theory and some Monte Carlo results.Comment: 33 pages, 10 figures; minor corrections, reference added. arXiv admin
note: substantial text overlap with arXiv:1007.088

### Relationships between log N-log S and celestial distribution of gamma-ray bursts

The apparent conflict between log N-log S curve and isotropic celestial distribution of the gamma ray bursts is discussed. A possible selection effect due to the time profile of each burst is examined. It is shown that the contradiction is due to this selection effect of the gamma ray bursts

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