862 research outputs found
A method for putting chiral fermions on the lattice
We describe a method to put chiral gauge theories on the lattice. Our method
makes heavy use of the effective action for chiral fermions in the continuum,
which is in general complex. As an example we discuss the chiral Schwinger
model.Comment: 4 pages, HLRZ 92-8
Macroscopoic Three-Loop Amplitudes and the Fusion Rules from the Two-Matrix Model
From the computation of three-point singlet correlators in the two-matrix
model, we obtain an explicit expression for the macroscopic three-loop
amplitudes having boundary lengths in the case of
the unitary series coupled to two-dimensional gravity. The sum
appearing in this expression is found to conform to the structure of the CFT
fusion rules while the summand factorizes through a product of three modified
Bessel functions. We briefly discuss a possible generalization of these
features to macroscopic -loop amplitudes.Comment: 9 pages, no figure, late
Darboux Transformation for the Manin-Radul Supersymmetric KdV equation
In this paper we present a vectorial Darboux transformation, in terms of
ordinary determinants, for the supersymmetric extension of the Korteweg-de
Vries equation proposed by Manin and Radul. It is shown how this transformation
reduces to the Korteweg-de Vries equation. Soliton type solutions are
constructed by dressing the vacuum and we present some relevant plots.Comment: 14 pp, 2 figures, AMS-LaTeX, to appear in Phys. Lett.
Massive Hyper-Kahler Sigma Models and BPS Domain Walls
With the non-Abelian Hyper-Kahler quotient by U(M) and SU(M) gauge groups, we
give the massive Hyper-Kahler sigma models that are not toric in the N=1
superfield formalism. The U(M) quotient gives N!/[M! (N-M)!] (N is a number of
flavors) discrete vacua that may allow various types of domain walls, whereas
the SU(M) quotient gives no discrete vacua. We derive BPS domain wall solution
in the case of N=2 and M=1 in the U(M) quotient model.Comment: 16 pages, 1 figure, contribution to the Proceedings of the
International Conference on "Symmetry Methods in Physics (SYM-PHYS10)" held
at Yerevan, Armenia, 13-19 Aug. 200
-Virasoro Algebra and the Point-Splitting
It is shown that a particular -deformation of the Virasoro algebra can be
interpreted in terms of the -local field and the Schwinger-like
point-splitted Virasoro currents, quadratic in . The -deformed
Virasoro algebra possesses an additional index , which is directly
related to point-splitting of the currents. The generators in the -deformed
case are found to exactly reproduce the results obtained by probing the fields
(string coordinate) and (string momentum) with the
non-splitted Virasoro generators and lead to a particular representation of the
algebra characterized by the standard conformal dimension of
the field. Some remarks concerning the -vertex operator for the interacting
-string theory are made.Comment: 17 pages, Late
Large N and double scaling limits in two dimensions
Recently, the author has constructed a series of four dimensional
non-critical string theories with eight supercharges, dual to theories of light
electric and magnetic charges, for which exact formulas for the central charge
of the space-time supersymmetry algebra as a function of the world-sheet
couplings were obtained. The basic idea was to generalize the old matrix model
approach, replacing the simple matrix integrals by the four dimensional matrix
path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov
critical points by the Argyres-Douglas critical points. In the present paper,
we study qualitatively similar toy path integrals corresponding to the two
dimensional N=2 supersymmetric non-linear sigma model with target space CP^n
and twisted mass terms. This theory has some very strong similarities with N=2
super Yang-Mills, including the presence of critical points in the vicinity of
which the large n expansion is IR divergent. The model being exactly solvable
at large n, we can study non-BPS observables and give full proofs that double
scaling limits exist and correspond to universal continuum limits. A complete
characterization of the double scaled theories is given. We find evidence for
dimensional transmutation of the string coupling in some non-critical string
theories. We also identify en passant some non-BPS particles that become
massless at the singularities in addition to the usual BPS states.Comment: 38 pages, including an introductory section that makes the paper
self-contained, two figures and one appendix; v2: typos correcte
Towards N=1 Super-Yang-Mills on the Lattice
We consider the lattice regularization of N=1 supersymmetric Yang--Mills
theory with Wilson fermions. This formulation breaks supersymmetry at any
finite lattice spacing; we discuss how Ward identities can be used to define a
supersymmetric continuum limit, which coincides with the point where the gluino
becomes massless. As a first step towards the understanding of the zero
gluino-mass limit, we present results on the quenched low-lying spectrum of
SU(2) N=1 Super-Yang--Mills, at on a lattice, in
the OZI approximation. Our results, in spite of the quenched and OZI
approximations, are in remarkable agreement with theoretical predictions in the
supersymmetric theory, for the states with masses which are not expected to get
a large contribution from fermion loops.Comment: 25 Latex pages, 5 figure
Monopole and Dyon Bound States in N=2 Supersymmetric Yang-Mills Theories
We study the existence of monopole bound states saturating the BPS bound in
N=2 supersymmetric Yang-Mills theories. We describe how the existence of such
bound states relates to the topology of index bundles over the moduli space of
BPS solutions. Using an index theorem, we prove the existence of certain
BPS states predicted by Seiberg and Witten based on their study of the vacuum
structure of N=2 Yang-Mills theories.Comment: 34 pages, harvma
On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
By invoking the concept of twisted Poincar\' e symmetry of the algebra of
functions on a Minkowski space-time, we demonstrate that the noncommutative
space-time with the commutation relations ,
where is a {\it constant} real antisymmetric matrix, can be
interpreted in a Lorentz-invariant way. The implications of the twisted
Poincar\'e symmetry on QFT on such a space-time is briefly discussed. The
presence of the twisted symmetry gives justification to all the previous
treatments within NC QFT using Lorentz invariant quantities and the
representations of the usual Poincar\'e symmetry.Comment: 12 pages, one reference adde
Gravitational shocks as a key ingredient of Gamma-Ray Bursts
We identify a novel physical mechanism that may be responsible for energy
release in -ray bursts. Radial perturbations in the neutron core,
induced by its collision with collapsing outer layers during the early stages
of supernova explosions, can trigger a gravitational shock, which can readily
eject a small but significant fraction of the collapsing material at
ultra-relativistic speeds. The development of such shocks is a strong-field
effect arising in near-critical collapse in General Relativity and has been
observed in numerical simulations in various contexts, including in particular
radially perturbed neutron star collapse, albeit for a tiny range of initial
conditions. Therefore, this effect can be easily missed in numerical
simulations if the relevant parameter space is not exhaustively investigated.
In the proposed picture, the observed rarity of -ray bursts would be
explained if the relevant conditions for this mechanism appear in only about
one in every core collapse supernovae. We also mention the
possibility that near-critical collapse could play a role in powering the
central engines of Active Galactic Nuclei.Comment: 9 pages, 3 figure
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