267 research outputs found
Locality, Causality and Noncommutative Geometry
We analyse the causality condition in noncommutative field theory and show
that the nonlocality of noncommutative interaction leads to a modification of
the light cone to the light wedge. This effect is generic for noncommutative
geometry. We also check that the usual form of energy condition is violated and
propose that a new form is needed in noncommutative spacetime. On reduction
from light cone to light wedge, it looks like the noncommutative dimensions are
effectively washed out and suggests a reformulation of noncommutative field
theory in terms of lower dimensional degree of freedom. This reduction of
dimensions due to noncommutative geometry could play a key role in explaining
the holographic property of quantum gravity.Comment: 16 pages, LaTeX, 4 figure
Superembedding methods for 4d N=1 SCFTs
We extend SO(4,2) covariant lightcone embedding methods of four-dimensional
CFTs to N=1 superconformal field theory (SCFT). Manifest superconformal
SU(2,2|1) invariance is achieved by realizing 4D superconformal space as a
surface embedded in the projective superspace spanned by certain complex chiral
supermatrices. Because SU(2,2|1) acts linearly on the ambient space, the
constraints on correlators implied by superconformal Ward identities are
automatically solved in this formalism. Applications include new, compact
expressions for correlation functions containing one anti-chiral superfield and
arbitrary chiral superfield insertions, and manifestly invariant expressions
for the superconformal cross-ratios that parametrize the four-point function of
two chiral and two anti-chiral fields. Superconformal expressions for the
leading singularities in the OPE of chiral and anti-chiral operators are also
given. Because of covariance, our expressions are valid in any superconformally
flat background, e.g., AdS_4 or R times S^3.Comment: 33 pages, clarification of constraints, version to appear in PR
One-loop unitarity of scalar field theories on Poincare invariant commutative nonassociative spacetimes
We study scalar field theories on Poincare invariant commutative
nonassociative spacetimes. We compute the one-loop self-energy diagrams in the
ordinary path integral quantization scheme with Feynman's prescription, and
find that the Cutkosky rule is satisfied. This property is in contrast with
that of noncommutative field theory, since it is known that noncommutative
field theory with space/time noncommutativity violates unitarity in the above
standard scheme, and the quantization procedure will necessarily become
complicated to obtain a sensible Poincare invariant noncommutative field
theory. We point out a peculiar feature of the non-locality in our
nonassociative field theories, which may explain the property of the unitarity
distinct from noncommutative field theories. Thus commutative nonassociative
field theories seem to contain physically interesting field theories on
deformed spacetimes.Comment: 25 pages, 9 figures ; appendix and references adde
Noncommutative Einstein-AdS Gravity in three Dimensions
We present a Lorentzian version of three-dimensional noncommutative
Einstein-AdS gravity by making use of the Chern-Simons formulation of pure
gravity in 2+1 dimensions. The deformed action contains a real, symmetric
metric and a real, antisymmetric tensor that vanishes in the commutative limit.
These fields are coupled to two abelian gauge fields. We find that this theory
of gravity is invariant under a class of transformations that reduce to
standard diffeomorphisms once the noncommutativity parameter is set to zero.Comment: 11 pages, LaTeX, minor errors corrected, references adde
On Black Holes and Cosmological Constant in Noncommutative Gauge Theory of Gravity
Deformed Reissner-Nordstr\"om, as well as Reissner-Nordstr\"om de Sitter,
solutions are obtained in a noncommutative gauge theory of gravitation. The
gauge potentials (tetrad fields) and the components of deformed metric are
calculated to second order in the noncommutativity parameter. The solutions
reduce to the deformed Schwarzschild ones when the electric charge of the
gravitational source and the cosmological constant vanish. Corrections to the
thermodynamical quantities of the corresponding black holes and to the radii of
different horizons have been determined. All the independent invariants, such
as the Ricci scalar and the so-called Kretschmann scalar, have the same
singularity structure as the ones of the usual undeformed case and no smearing
of singularities occurs. The possibility of such a smearing is discussed. In
the noncommutative case we have a local disturbance of the geometry around the
source, although asymptotically at large distances it becomes flat.Comment: Based on a talk given at the International Conference on Fundamental
and Applied Research in Physics "Farphys 2007", 25-28 October 2007, Iasi,
Romani
One-loop effects in a self-dual planar noncommutative theory
We study the UV properties, and derive the explicit form of the one-loop
effective action, for a noncommutative complex scalar field theory in 2+1
dimensions with a Grosse-Wulkenhaar term, at the self-dual point. We also
consider quantum effects around non-trivial minima of the classical action
which appear when the potential allows for the spontaneous breaking of the U(1)
symmetry. For those solutions, we show that the one-loop correction to the
vacuum energy is a function of a special combination of the amplitude of the
classical solution and the coupling constant.Comment: Version to appear in JHE
Unitarity of noncommutative field theories from string theory
We improve the study of the lack of perturbative unitarity of noncommutative
space-time quantum field theories derived from open string theory in electric
backgrounds, enforcing the universality of the mechanism by which a tachyonic
branch cut appears when the Seiberg-Witten limit freezes the string in an
unstable vacuum. The main example is realized in the context of the on-shell
four-tachyon amplitude of the bosonic string, and the dependence of the
phenomenon on the brane-worldvolume dimension is analysed. We discuss the
possibility of a proof in superstring theory, and finally mention the NCOS
limit in this framework.Comment: 8 pages, no figures. Work done in collaboration with A. Bassetto and
R. Valandro (Padua Univ.). Submitted for the proceedings of the conference
"Spacetime and Fundamental Interactions: Quantum Aspects. A conference to
honour A.P.Balachandran's 65th birthday", Vietri, 26-31 May 200
Graviton Propagators on Fuzzy G/H
We describe closed string modes by open Wilson lines in noncommutative (NC)
gauge theories on compact fuzzy G/H in IIB matrix model. In this construction
the world sheet cut-off is related to the spacetime cut-off since the string
bit of the symmetric traced Wilson line carries the minimum momentum on G/H. We
show that the two point correlation functions of graviton type Wilson lines in
4 dimensional NC gauge theories behave as 1/(momentum)^2. This result suggests
that graviton is localized on D3-brane, so we can naturally interpret D3-branes
as our universe. Our result is not limited to D3-brane system, and we
generalize our analysis to other dimensions and even to any topology of D-brane
worldvolume within fuzzy G/H.Comment: 22 pages, 1 figure. minor correction
One-loop renormalization of general noncommutative Yang-Mills field model coupled to scalar and spinor fields
We study the theory of noncommutative U(N) Yang-Mills field interacting with
scalar and spinor fields in the fundamental and the adjoint representations. We
include in the action both the terms describing interaction between the gauge
and the matter fields and the terms which describe interaction among the matter
fields only. Some of these interaction terms have not been considered
previously in the context of noncommutative field theory. We find all
counterterms for the theory to be finite in the one-loop approximation. It is
shown that these counterterms allow to absorb all the divergencies by
renormalization of the fields and the coupling constants, so the theory turns
out to be multiplicatively renormalizable. In case of 1PI gauge field functions
the result may easily be generalized on an arbitrary number of the matter
fields. To generalize the results for the other 1PI functions it is necessary
for the matter coupling constants to be adapted in the proper way. In some
simple cases this generalization for a part of these 1PI functions is
considered.Comment: 1+26 pages, figures using axodraw, clarifications adde
Thermofield Dynamics for Twisted Poincare-Invariant Field Theories: Wick Theorem and S-matrix
Poincare invariant quantum field theories can be formulated on
non-commutative planes if the statistics of fields is twisted. This is
equivalent to state that the coproduct on the Poincare group is suitably
twisted. In the present work we present a twisted Poincare invariant quantum
field theory at finite temperature. For that we use the formalism of
Thermofield Dynamics (TFD). This TFD formalism is extend to incorporate
interacting fields. This is a non trivial step, since the separation in
positive and negative frequency terms is no longer valid in TFD. In particular,
we prove the validity of Wick's theorem for twisted scalar quantum field at
finite temperature.Comment: v1: 25 pages, no figure v2: references added; typos corrected; typo
in title correcte
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