Horacio Oscar Girotti

A Consistent noncommutative field theory: The Wess-Zumino model

Abstract We show that the noncommutative Wess–Zumino model is renormalizable to all orders of perturbation theory. The noncommutative scalar potential by itself is non-renormalizable but the Yukawa terms demanded by supersymmetry improve the situation turning the theory into a renormalizable one. As in the commutative case, there are neither quadratic nor linear divergences. Hence, the IR/UV mixing does not give rise to quadratic infrared poles.

THE NONCOMMUTATIVE SUPERSYMMETRIC NONLINEAR SIGMA MODEL

We show that the noncommutativity of space–time destroys the renormalizability of the 1/N expansion of the O(N) Gross–Neveu model. A similar statement holds for the noncommutative nonlinear sigma model. However, we show that, up to the subleading order in 1/N expansion, the noncommutative supersymmetric O(N) nonlinear sigma model becomes renormalizable in D=3. We also show that dynamical mass generation is restored and there is no catastrophic UV/IR mixing. Unlike the commutative case, we find that the Lagrange multiplier fields, which enforce the supersymmetric constraints, are also renormalized. For D=2 the divergence of the four-point function of the basic scalar field, which in D=3 is absent, cannot be eliminated by means of a counterterm having the structure of a Moyal product.

Towards a consistent noncommutative supersymmetric Yang-Mills theory : superfield covariant analysis

Commutative four dimensional supersymmetric Yang-Mills (SYM) theory is known to be renormalizable for N=1,2, and finite for N=4. However, in the noncommutative version of the model the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of the N=1,2,4 noncommutative supersymmetric Yang-Mills theory with gauge group U(N) (NCSYM). We employ the covariant superfield framework to compute the one-loop corrections to the two- and three-point functions of the gauge superfield V. It is found that the cancellation of the harmful UV/IR infrared divergences only takes place in the fundamental representation of the gauge group. We argue that this is in agreement with the low energy limit of the open superstring in the presence of an external magnetic field. As expected, the planar sector of the two-point function of the V superfield exhibits UV divergences. They are found to cancel, in the Feynman gauge, for the maximally extended N=4 supersymmetric theory. This gives support to the belief that the N=4 NCSYM theory is UV finite.

The three-dimensional noncommutative nonlinear sigma model in superspace

Abstract We study the superspace formulation of the noncommutative nonlinear supersymmetric O ( N ) invariant sigma-model in 2+1 dimensions. We prove that the model is renormalizable to all orders of 1/ N and explicitly verify that the model is asymptotically free.

The Low Energy Limit of the Noncommutative Wess-Zumino Model

The non-commutative Wess-Zumino model is used as a prototype for studying the low energy behavior of a renormalizable non-commutative field theory. We start by deriving the potentials mediating the fermion-fermion and boson-boson interactions in the non-relativistic regime. The quantum counterparts of these potentials are afflicted by ordering ambiguities but we show that there exists an ordering prescription which makes them hermitean. For space/space noncommutativity it turns out that Majorana fermions may be pictured as rods oriented perpendicularly to the direction of motion showing a lack of locality, while bosons remain insensitive to the effects of the non commutativity. For time/space noncommutativity bosons and fermions can be regarded as rods oriented along the direction of motion. For both cases of noncommutativity the scattering state describes scattered waves, with at least one wave having negative time delay signalizing the underlying nonlocality. The superfield formulation of the model is used to compute the corresponding effective action in the one- and two-loop approximations. In the case of time/space noncommutativity, unitarity is violated in the relativistic regime. However, this does not preclude the existence of a unitary low energy limit.

On the finiteness of noncommutative supersymmetric QED3 in the covariant superfield formulation

The three-dimensional noncommutative supersymmetric QED is investigated within the superfield approach. We prove the absence of UV/IR mixing in the theory at any loop order and demonstrate its one-loop finiteness.

Horava-Lifshitz modifications of the Casimir effect

We study the modifications induced by spacetime anisotropy on the Casimir effect in the case of two parallel plates. Non-perturbative and perturbative regimes are analyzed. In the first case, the Casimir force either vanishes or it reverses its direction which, in any case, makes the proposal untenable. On the other hand, the perturbative model enables us to incorporate appropriately the effects of spacetime anisotropy.

Duality symmetry in the Schwarz-Sen model

The continuous extension of the discrete duality symmetry of the Schwarz-Sen model is studied. The corresponding infinitesimal generator Q turns out to be local, gauge invariant, and metric independent. Furthermore, Q commutes with all the conformal group generators. We also show that Q is equivalent to the nonlocal duality transformation generator found in the Hamiltonian formulation of Maxwell theory. We next consider the Batalin-Fradkin-Vilkovisky formalism for the Maxwell theory and demonstrate that requiring a local duality transformation leads us to the Schwarz-Sen formulation. The partition functions are shown to be the same, which implies the quantum equivalence of the two approaches. {copyright} {ital 1997} {ital The American Physical Society}

The fermion-fermion effective potential in the Maxwell-Chern-Simons theory

Abstract The effective nonrelativistic potential V T describing the fermion-fermion interaction in the Maxwell-Chern-Simons theory is derived to the lowest order in perturbation theory. As expected, V T is not invariant under parity and time-reversal transformations. The quantum dynamics generated by V T becomes exactly solvable at the limits where either the Maxwell or the Chern-Simons terms disappear; in neither case electron-electron bound states show up. However, numerical calculations indicate that fermion-fermion bound states do exist in the general case.

Anyons and singular gauge transformations

Abstract A (2+1)-dimensional theory of charged scalar particles coupled to an abelian gauge field with Chern-Simons term in the action is canonically quantized in the Coulomb and superaxial gauges. The gauge transformation linking these two gauges is shown to be singular. Then, the superaxial gauge excitations are found to obey fractional statistics. We demonstrate that this effect does not arise when the conventional term −1/4FμνFμν is present in the action.