417 research outputs found
Aspects of Group Field Theory
I review the basic ingredients of discretized gravity which motivate the
introduction of Group Field Theory. Thus I describe the GFT formulation of some
models and conclude with a few remarks on the emergence of noncommutative
structures in such models.Comment: Invited Talk at the conference: XX Fall Workshop on Geometry and
Physics, ICMAT, Madrid 2011. To be published in AIP Conference Proceeding
Temperature induced phase transitions in four fermion models in curved space-time
The large N limit of the Gross-Neveu model is here studied on manifolds with
constant curvature, at zero and finite temperature. Using the zeta-function
regularization, the phase structure is investigated for arbitrary values of the
coupling constant. The critical surface where the second order phase transition
takes place is analytically found for both the positive and negative curvature
cases. For negative curvature, where the symmetry is always broken at zero
temperature, the mass gap is calculated. The free energy density is evaluated
at criticality and the zero curvature and zero temperature limits are
discussed.Comment: Latex file, 24 pages, 3 eps figures. Minor corrections. To appear in
Nucl. Phys.
A field-theoretic approach to Spin Foam models in Quantum Gravity
We present an introduction to Group Field Theory models, motivating them on
the basis of their relationship with discretized BF models of gravity. We
derive the Feynmann rules and compute quantum corrections in the coherent
states basis.Comment: 16 pages, 3 figures. Proceedings of the Workshop on Non Commutative
Field Theory and Gravity, September 8-12, 2010 Corfu Greec
-Minkowski star product in any dimension from symplectic realization
We derive an explicit expression for the star product reproducing the
-Minkowski Lie algebra in any dimension . The result is obtained by
suitably reducing the Wick-Voros star product defined on
with . It is thus shown that the new star
product can be obtained from a Jordanian twist.Comment: published versio
Matrix Bases for Star Products: a Review
We review the matrix bases for a family of noncommutative products
based on a Weyl map. These products include the Moyal product, as well as the
Wick-Voros products and other translation invariant ones. We also review the
derivation of Lie algebra type star products, with adapted matrix bases. We
discuss the uses of these matrix bases for field theory, fuzzy spaces and
emergent gravity
Three Dimensional Gross-Neveu Model on Curved Spaces
The large N limit of the 3-d Gross-Neveu model is here studied on manifolds
with positive and negative constant curvature. Using the -function
regularization we analyze the critical properties of this model on the spaces
and . We evaluate the free energy density, the
spontaneous magnetization and the correlation length at the ultraviolet fixed
point. The limit , which is interpreted as the zero temperature
limit, is also studied.Comment: 24 pages, LaTeX, two .eps figure
The Gribov problem in Noncommutative gauge theory
After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon
related to the topology of the bundle of gauge connections, we show that there
is a similar feature for noncommutative QED over Moyal space, despite the
structure group being Abelian, and we exhibit an infinite number of solutions
for the equation of Gribov copies. This is a genuine effect of noncommutative
geometry which disappears when the noncommutative parameter vanishes.Comment: 14 pages. Prepared for the XXV International Fall Workshop on
Geometry and Physics, Instituto de Estructura de la Materia (CSIC) Madrid,
Spain August 29 - September 02, 201
Noncommutative field theories on : Towards UV/IR mixing freedom
We consider the noncommutative space , a deformation of
the algebra of functions on which yields a "foliation" of
into fuzzy spheres. We first construct a natural matrix base
adapted to . We then apply this general framework to the
one-loop study of a two-parameter family of real-valued scalar noncommutative
field theories with quartic polynomial interaction, which becomes a non-local
matrix model when expressed in the above matrix base. The kinetic operator
involves a part related to dynamics on the fuzzy sphere supplemented by a term
reproducing radial dynamics. We then compute the planar and non-planar 1-loop
contributions to the 2-point correlation function. We find that these diagrams
are both finite in the matrix base. We find no singularity of IR type, which
signals very likely the absence of UV/IR mixing. We also consider the case of a
kinetic operator with only the radial part. We find that the resulting theory
is finite to all orders in perturbation expansion.Comment: 31 pages, 4 figures. Improved version. Sections 5.1 and 5.2 have been
clarified. A minor error corrected. References adde
A novel approach to non-commutative gauge theory
We propose a field theoretical model defined on non-commutative space-time
with non-constant non-commutativity parameter , which satisfies two
main requirements: it is gauge invariant and reproduces in the commutative
limit, , the standard gauge theory. We work in the slowly
varying field approximation where higher derivatives terms in the star
commutator are neglected and the latter is approximated by the Poisson bracket,
. We derive an explicit expression for both the NC
deformation of Abelian gauge transformations which close the algebra
, and the NC field strength ,
covariant under these transformations, . NC
Chern-Simons equations are equivalent to the requirement that the NC field
strength, , should vanish identically. Such equations are
non-Lagrangian. The NC deformation of Yang-Mills theory is obtained from the
gauge invariant action, . As guiding example, the case of
-like non-commutativity, corresponding to rotationally invariant NC
space, is worked out in detail.Comment: 16 pages, no figures. Minor correction
Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory
By twisting the commutation relations between creation and annihilation
operators, we show that quantum conformal invariance can be implemented in the
2-d Moyal plane. This is an explicit realization of an infinite dimensional
symmetry as a quantum algebra.Comment: 10 pages. Text enlarged. References adde
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