Gordon W. Semenoff

BMN Correlators and Operator Mixing in N=4 Super Yang-Mills Theory

Correlation functions in perturbative N = 4 supersymmetric Yang-Mills theory are examined in the Berenstein-Maldacena-Nastase (BMN) limit. We demonstrate that non-extremal four-point functions of chiral primary fields are ill-defined in that limit. This lends support to the assertion that only gauge theoretic two-point functions should be compared to pp-wave strings. We further refine the analysis of the recently discovered non-planar corrections to the planar BMN limit. In particular, a full resolution to the genus one operator mixing problem is presented, leading to modifications in the map between BMN operators and string states. We give a perturbative construction of the correct operators and we identify their anomalous dimensions. We also distinguish symmetric, anti-symmetric and singlet operators and find, interestingly, the same torus anomalous dimension for all three. Finally, it is discussed how operator mixing effects modify three point functions at the classical level and, at one loop, allow us to recover conformal invariance.

Finite size Giant Magnons in the string dual of N=6 superconformal Chern-Simons theory

We find the exact solution for a finite size Giant Magnon in the SU(2) × SU(2) sector of the string dual of the = 6 superconformal Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. The finite size Giant Magnon solution consists of two magnons, one in each SU(2). In the infinite size limit this solution corresponds to the Giant Magnon solution of arXiv:0806.4959. The magnon dispersion relation exhibits finite-size exponential corrections with respect to the infinite size limit solution.

Discontinuities of green functions in field theory at finite temperature and density

Abstract Extending some previous work on Cutkosky rules at finite temperature and density in a real time formalism, we consider here the case that all external lines of a Feynman graph are physical. We find the corresponding rules simplify considerably, although still do not admit an interpretation in terms of cutting a graph. An analysis of the relationship between the imaginary part of a self-energy graph and decay amplitudes suggests that the graphs which cannot be cut correspond to contributions from the ghost field necessary if real time Feynman rules are used. We also discuss, crudely speaking, where one can “start” and “end” in time in a Feynman graph at finite temperature and density.

Two-loop analysis of non-Abelian Chern-Simons theory.

Perturbative renormalization of a non-Abelian Chern-Simons gauge theory is examined. It is demonstrated by explicit calculation that, in the pure Chern-Simons theory, the [beta] function for the coefficient of the Chern-Simons term vanishes to three-loop order. Both dimensional regularization and regularization by introducing a conventional Yang-Mills term in the action are used. It is shown that dimensional regularization is not gauge invariant at two loops. A variant of this procedure, similar to regularization by dimensional reduction used in supersymmetric field theories, is shown to obey the Slavnov-Taylor identity to two loops and gives no renormalization of the Chern-Simons term. Regularization with the Yang-Mills term yields a finite integer-valued renormalization of the coefficient of the Chern-Simons term at one loop, and we conjecture no renormalization at higher order. We also examine the renormalization of Chern-Simons theory coupled to matter. We show that in the non-Abelian case the Chern-Simons gauge field as well as the matter fields require infinite renormalization at two loops and therefore obtain nontrivial anomalous dimensions. We show that the [beta] function for the gauge coupling constant is zero to two-loop order, consistent with the topological quantization condition for this constant.

Gauge invariant finite size spectrum of the giant magnon

It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform light-cone gauge parameter. The resulting finite size effects are exponentially small in the R-charge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model.

Wilson loops in N=4 SYM and fermion droplets

The matrix models which are conjectured to compute the circle Wilson loop and its correlator with chiral primary operators are mapped onto normal matrix models. A fermion droplet picture analogous to the well-known one for chiral primary operators is shown to emerge in the large N limit. Several examples are computed. We find an interesting selection rule for the correlator of a single trace Wilson loop with a chiral primary operator. It can be non-zero only if the chiral primary is in a representation with a single hook. We show that the expectation value of the Wilson loop in a large representation labelled by a Young diagram with a single row has a first order phase transition between a regime where it is identical to a large column representation and a regime where it is a large wrapping number single trace Wilson loop.

Finite size giant magnon

The quantization of the giant magnon away from the infinite size limit is discussed. We argue that this quantization inevitably leads to string theory on a Z{sub M} orbifold of S{sup 5}. This is shown explicitly and examined in detail in the near plane-wave limit.

Domain walls in gapped graphene

The electronic properties of a particular class of domain walls in gapped graphene are investigated. We show that they can support midgap states which are localized in the vicinity of the domain wall and propagate along its length. With a finite density of domain walls, these states can alter the electronic properties of gapped graphene significantly. If the midgap band is partially filled, the domain wall can behave like a one-dimensional metal embedded in a semiconductor and could potentially be used as a single-channel quantum wire.

Exotic spin and statistics in (2+1)-dimensional canonical quantum field theory

Canonical quantization is used to examine the relationship between the addition of a Chern-Simons topological mass term to the action of a (2+1)-dimensional quantum field theory and exotic spin and statistics of elementary quanta. We argue that topologically massive electrodynamics is solved in the long wavelength limit by multi-valued fields with anomalous spin and which create quantum states which have exotic exchange statistics. The quantum states with N particles represent the braid group BN. We examine the implications of our results for the O(3) nonlinear sigma model where the topological current is coupled to topologically massive electrodynamics and the charge carriers are topological solitons.

Wilson loops in SYM theory: From weak to strong coupling

Abstract We review calculations of Wilson loops in N = 4 supersymmetric Yang-Mills theory using both the AdS/CFT correspondence and perturbation theory. We emphasize the cases in which resummation of perturbative series give exact results. Agreement of these result with string theory predictions is a stringent test of the AdS/CFT correspondence.