369 research outputs found
Lattice Supersymmetry via Twisting
We describe how the usual supercharges of extended supersymmetry may be {\it
twisted} to produce a BRST-like supercharge . The usual supersymmetry
algebra is then replaced by a twisted algebra and the action of the twisted
theory is shown to be generically -exact. In flat space the twisting
procedure can be regarded as a change of variables carrying no physical
significance. However, the twisted theories can often be transferred to the
lattice while preserving the twisted supersymmetry. As an example we construct
a lattice version of the two-dimensional supersymmetric sigma model.Comment: Contribution to Lattice2004(theory
Supersymmetric lattices
Discretization of supersymmetric theories is an old problem in lattice field
theory. It has resisted solution until quite recently when new ideas drawn from
orbifold constructions and topological field theory have been brought to bear
on the question. The result has been the creation of a new class of lattice
gauge theory in which the lattice action is invariant under one or more
supersymmetries. The resultant theories are local and free of doublers and in
the case of Yang-Mills theories also possess exact gauge invariance. In
principle they form the basis for a truly non-perturbative definition of the
continuum supersymmetric field theory. In this talk these ideas are reviewed
with particular emphasis being placed on super Yang-Mills theory.Comment: Plenary talk at the symposium Quantum Theory and Symmetries,
Lexington, Kentucky, July 2009. References adde
Dirac-K\"{a}hler fermions and exact lattice supersymmetry
We discuss a new approach to putting supersymmetric theories on the lattice.
The basic idea is to start from a {\it twisted} formulation of the underlying
supersymmetric theory in which the fermions are represented as grassmann valued
antisymmetric tensor fields. The original supersymmetry algebra is replaced by
a twisted algebra which contains a scalar nilpotent supercharge .
Furthermore the action of the theory can then be written as the -variation
of some function. The case of super Yang-Mills theory in two
dimensions is discussed in some detail. We then present our proposal for
discretizing this theory and derive the resultant lattice action. The latter is
local, free of spectrum doubling, gauge invariant and preserves the scalar
supercharge invariance exactly. Some preliminary numerical results are then
presented. The approach can be naturally generalized to yield a lattice action
for super Yang-Mills in four dimensions.Comment: 22 pages, 3 figures. Plenary talk given at Lattice 2005 Dublin July
25-30. 1 reference correcte
Twisted lattice supersymmetry and applications to AdS/CFT
I review recent approaches to constructing supersymmetric lattice theories
focusing in particular on the concept of topological twisting. The latter
technique is shown to expose a nilpotent, scalar supersymmetry which can be
implemented exactly in the lattice theory. Using these ideas a lattice action
for super Yang-Mills in four dimensions can be written down
which is gauge invariant, free of fermion doublers and respects one out of a
total of 16 continuum supersymmetries. It is shown how these exact symmetries
together with the large point group symmetry of the lattice strongly constrain
the possible counterterms needed to renormalize the theory and hence determine
how much residual fine tuning will be needed to restore all supersymmetries in
the continuum limit. We report on progress to study these renormalization
effects at one loop. We go on to give examples of applications of these
supersymmetric lattice theories to explore the connections between gauge
theories and gravity.Comment: 16 pages. Plenary talk at Lattice 201
Notes on (twisted) lattice supersymmetry
We describe a new approach to the problem of putting supersymmetric theories
on the lattice. The basic idea is to discretize a {\it twisted} formulation of
the supersymmetric theory. For certain theories with extended supersymmetry
these twisted formulations contain only integer spin fields. The twisting
exposes a scalar nilpotent supercharge which generates an exact lattice
symmetry. We gives examples from quantum mechanics, sigma models and Yang-Mills
theories.Comment: Summary of lectures given at the Summer Institute 2005 Fuji-Yoshida,
Japan August 11-18, 200
On the restoration of supersymmetry in twisted two-dimensional lattice Yang-Mills theory
We study a discretization of super Yang-Mills theory which
possesses a single exact supersymmetry at non-zero lattice spacing. This
supersymmetry arises after a reformulation of the theory in terms of {\it
twisted} fields. In this paper we derive the action of the other twisted
supersymmetries on the component fields and study, using Monte Carlo
simulation, a series of corresponding Ward identities. Our results for SU(2)
and SU(3) support a restoration of these additional supersymmetries without
fine tuning in the infinite volume continuum limit. Additionally we present
evidence supporting a restoration of (twisted) rotational invariance in the
same limit. Finally we have examined the distribution of scalar field
eigenvalues and find evidence for power law tails extending out to large
eigenvalue. We argue that these tails indicate that the classical moduli space
does not survive in the quantum theory.Comment: 35 pages, 14 figures, 18 tables. Results section rewritten to include
discussion of phase quenching, continuum scaling and thermal boundary
conditions. Version to be published in JHE
Exact Lattice Supersymmetry from Topological Field Theory
We discuss the connection between supersymmetric field theories and
topological field theories and show how this connection may be used to
construct local lattice field theories which maintain an exact supersymmetry.
It is shown how metric independence of the continuum topological field theory
allows us to derive the lattice theory by blocking out of the continuum in a
deformed geometry. This, in turn, allows us to prove the cut-off independence
of certain supersymmetric Ward identities.Comment: Lattice2003(theory
Three dimensional lattice gravity as supersymmetric Yang-Mills theory
We argue that a certain twisted supersymmetric Yang-Mills theory in three
dimensions with gauge group SU(2) possesses a set of topological observables
whose expectation values can be computed in a related Chern Simons theory. This
Chern Simons theory has been proposed as a definition of three dimensional
Euclidean quantum gravity. Since the YM theory admits a discretization which
preserves the values of topological observables we conjecture that it can be
used as a non-perturbative definition of the quantum gravity theory.Comment: 8 pages. Contribution to Lattice 201
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