M. M. Sheikh-Jabbari

Hydrogen atom spectrum and the Lamb shift in noncommutative QED

We have calculated the energy levels of the hydrogen atom as well as the Lamb shift within the noncommutative quantum electrodynamics theory. The results show deviations from the usual QED both on the classical and the quantum levels. On both levels, the deviations depend on the parameter of space/space noncommutativity.

Noncommutative geometry from strings and branes

Noncommutative torus compactification of Matrix model is shown to be a direct consequence of quantization of the open strings attached to a D-membrane with a non-vanishing background B field. We calculate the BPS spectrum of such a brane system using both string theory results and DBI action. The DBI action leads to a new transformation property of the compactification radii under the SL(2,)N transformations.

Dirac quantization of open strings and noncommutativity in branes

Abstract We apply the Dirac bracket quantization to open strings attached to branes in the presence of background antisymmetric field and recover an inherent noncommutativity in the internal coordinates of the brane.

Supergravity and large N noncommutative field theories

We consider systems of Dp-branes in the presence of a nonzero B field. We study the corresponding supergravity solutions in the limit where the branes worldvolume theories decouple from gravity. These provide dual descriptions of large N noncommutative field theories. We analyse the phase structure of the theories and the validity of the different description. We provide evidence that in the presence of a nonzero B field the worldvolume theory of D6 branes may decouple from gravity. We analyse the systems of M5 branes and NS5 branes in the presence of a nonzero C field and nonzero RR fields, respectively. Finally, we study the Wilson loops (surfaces) using the dual descriptions.

Gauge fields and inflation

Abstract The isotropy and homogeneity of the cosmic microwave background (CMB) favors “scalar driven” early Universe inflationary models. However, gauge fields and other non-scalar fields are far more common at all energy scales, in particular at high energies seemingly relevant to inflation models. Hence, in this review we consider the role and consequences, theoretical and observational, that gauge fields can have during the inflationary era. Gauge fields may be turned on in the background during inflation, or may become relevant at the level of cosmic perturbations. There have been two main classes of models with gauge fields in the background, models which show violation of the cosmic no-hair theorem and those which lead to isotropic FLRW cosmology, respecting the cosmic no-hair theorem. Models in which gauge fields are only turned on at the cosmic perturbation level, may source primordial magnetic fields. We also review specific observational features of these models on the CMB and/or the primordial cosmic magnetic fields. Our discussions will be mainly focused on the inflation period, with only a brief discussion on the post inflationary (p)reheating era.

Open strings in a B-field background as electric dipoles

Abstract Studying dynamics of open strings attached to a D2-brane in a NS two form field background, we find that these open strings act as dipoles of U (1) gauge field of the brane. This provides an string theoretic description of the flux modifications needed for the DBI action on noncommutative torus.

Noncommutative Φ4 theory at two loops

We study perturbative aspects of noncommutative field theories. This work is arranged in two parts. First, we review noncommutative field theories in general and discuss both canonical and path integral quantization methods. In the second part, we consider the particular example of noncommutative Φ4 theory in four dimensions and work out the corresponding effective action and discuss renormalizability of the theory, up to two loops.

What is a chiral 2d CFT? And what does it have to do with extremal black holes?

The near horizon limit of the extremal BTZ black hole is a “self-dual orbifold” of AdS3. This geometry has a null circle on its boundary, and thus the dual field theory is a Discrete Light Cone Quantized (DLCQ) two dimensional CFT. The same geometry can be compactified to two dimensions giving AdS2 with a constant electric field. The kinematics of the DLCQ show that in a consistent quantum theory of gravity in these backgrounds there can be no dynamics in AdS2, which is consistent with older ideas about instabilities in this space. We show how the necessary boundary conditions eliminating AdS2 fluctuations can be implemented, leaving one copy of a Virasoro algebra as the asymptotic symmetry group. Our considerations clarify some aspects of the chiral CFTs appearing in proposed dual descriptions of the near-horizon degrees of freedom of extremal black holes.

Noncommutative gauge field theories: A No go theorem

Abstract Studying the general structure of the noncommutative (NC) local groups, we prove a no-go theorem for NC gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: (1) the local NC u(n) algebra only admits the irreducible n×n matrix-representation. Hence the gauge fields are in n×n matrix form, while the matter fields can only be in fundamental, adjoint or singlet states; (2) for any gauge group consisting of several simple-group factors, the matter fields can transform nontrivially under at most two NC group factors. In other words, the matter fields cannot carry more than two NC gauge group charges. This no-go theorem imposes strong restrictions on the NC version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED.

Noncommutative SO(n) and Sp(n) gauge theories

Abstract We study the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups. We find out that this is possible, since we are allowed to define orthogonal and symplectic subgroups of noncommutative unitary gauge transformations even though the gauge potentials and gauge transformations are not valued in the orthogonal and symplectic subalgebras of the Lie algebra of antihermitean matrices. Our construction relies on an anti-automorphism of the basic noncommutative algebra of functions which generalizes the charge conjugation operator of ordinary field theory. We show that the corresponding noncommutative picture from low energy string theory is obtained via orientifold projection in the presence of a non-trivial NSNS B field.