A Chern-Simons effective field theory for the Pfaffian quantum Hall state

We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU(2)₂ Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chem-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at v = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.     

Holographic description of large N gauge theory

Based on the earlier work [S.-S. Lee, Nucl. Rev. B 832 (2010) 567], we derive a holographic dual for the D-dimensional U(N) lattice gauge theory from a first principle construction. The resulting theory is a lattice field theory of closed loops, dubbed as lattice loop field theory which is defined on a (D+1)-dimensional space. The lattice loop field theory is well defined non-perturbatively, and it becomes weakly coupled and local in the large N limit with a large ?t Hooft coupling.     

From noncommutative κ-Minkowski to Minkowski space–time

We show that free κ-Minkowski space field theory, discussed in the context of κ-Poincaré algebra and Doubly Special Relativity is equivalent to a relativistically invariant free field theory on Minkowski space–time. The field theory we obtain has in spectrum a relativistic mode of arbitrary mass m and a Planck mass tachyon. We show that while the energy–momentum for the relativistic mode is essentially the standard one, it diverges for the tachyon, so that there are no asymptotic tachyonic states in the theory. It also follows that the dispersion relation is not modified, so that, in particular, in this theory the speed of light is energy-independent.     

Interpretation of Einstein's theory of gravitation including the cosmological term as a de Sitter-invariant field theory on the de Sitter space

In order to remove the singular nature of Einstein's theory of gravitation including theΛ term, within the domain of field theories, it is shown that this theory can be consistently interpreted as a field theory on the fixed de Sitter space, invariant with respect to the de Sitter groupO(4,1). The corresponding field equations as well as the equations of motion are derived, their structural properties are discussed, and they are integrated for a spherical mass source of the field.     

Mean field and Monte Carlo studies of SU(N) chiral models in three dimensions

SU(N) chiral models defined on three-dimensional cubic lattices arestudied using mean field and Monte Carlo techniques. Mean field theory predicts first-order transitions for all finite N greater than two. The mean field estimates of the transition temperature and discontinuity of the order parameter are in good agreement with computer simulations for N = 3 and 4. The N → ∞ limit of mean field theory has a first-order phase transition.     

Gauge fields and interactions in matrix string theory

It is shown that all possible N sheeted coverings of the cylinder are contained in type IIA matrix string theory as non-trivial gauge field configurations. Using these gauge field configurations as backgrounds the large N limit is shown to lead to the type IIA conformal field theory defined on the corresponding Riemann surfaces. The sum over string diagrams is identified as the sum over non-trivial gauge backgrounds of the SYM theory.     

Stochastic quantization of supersymmetric field theory

The Parisi-Wu stochastic quantization method is applied to supersymmetric field theory. The Langevin equation, which reproduces the Green functions of euclidean field theory, is written in terms of superfields. Supersymmetric U(1) theory under gauge fixing and the large N reduction in chiral SU(N) theory are discussed. Regularization based on the stochastic method is studied also.     

Generalised direct action and absorber theory of radiation

It is known that corresponding to a field theory of a tensor of arbitrary rank, there exists a direct-action theory under certain conditions. An attempt is therefore made to construct an explicit direct-action theory for a tensor field of rankN in such a form that the absorber theory of radiation may be worked out using the methods made so well known by Wheeler-Feynman and Hoyle-Narlikar. It is possible to recover the familiar electromagnetic theory corresponding to the case ofN = 1.     

Euclidean D-branes and higher-dimensional gauge theory

We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane—that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory—is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N_T = 2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold of G₂ holonomy.     

The renormalization group and the ϵ expansion

The modern formulation of the renormalization group is explained for both critical phenomena in classical statistical mechanics and quantum field theory. The expansion in ? = 4?d is explained [d is the dimension of space (statistical mechanics) or space-time (quantum field theory)]. The emphasis is on principles, not particular applications. Sections 1–8 provide a self-contained introduction at a fairly elementary level to the statistical mechanical theory. No background is required except for some prior experience with diagrams. In particular, a diagrammatic approximation to an exact renormalization group equation is presented in sections 4 and 5; sections 6–8 include the approximate renormalization group recursion formula and the Feyman graph method for calculating exponents. Sections 10–13 go deeper into renormalization group theory (section 9 presents a calculation of anomalous dimensions). The equivalence of quantum field theory and classical statistical mechanics near the critical point is established in section 10; sections 11–13 concern problems common to both subjects. Specific field theoretic references assume some background in quantum field theory. An exact renormalization group equation is presented in section 11; sections 12 and 13 concern fundamental topological questions.     

Analysis of the master equation for the Dicke model in squeezed vacua

The master equation for the reduced atomic density operator for the Dicke model (N_a 2-level atoms on the same single site) interacting with a broad-band squeezed vacuum state field is derived using operator reaction field theory. The analysis through reaction field theory is presented first of all for the normal vacuum and then for the squeezed vacuum, both within the Markov and Born approximations. In the case of the squeezed vacuum field a statistical decorrelation between matter and field variables is also necessarily adopted in order to close the system of equations: this is also the case for the broad-band black-body field, and the theory contrasts with that which employs projection operator techniques and uses weak coupling. Models involving a both axially symmetrical and wholly isotropic distribution of the squeezed vacuum modes are compared.     

The Haldane-Rezayi quantum Hall state and conformal field theory

We propose field theories for the bulk and edge of a quantum Hall state in the universality class of the Haldane-Rezayi wavefunction. The bulk theory is associated with the c = −2 conformal field theory. The topological properties of the state, such as the quasiparticle braiding statistics and ground state degeneracy on a torus, may be deduced from this conformal field theory. The 10-fold degeneracy on a torus is explained by the existence of a logarithmic operator in the c = −2 theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the c = 1 chiral Dirac fermion, which is related in a simple way to the c = −2 theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the SU(2) symmetry - which corresponds to the spin-rotational symmetry of the quantum Hall system - is manifest and non-local. We make predictions for the current-voltage characteristics for transport through point contacts.     

Double field formulation of Yang-Mills theory

Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge symmetries. In double field formulation, in a manifestly covariant manner our action couples a single O(D,D) vector potential to the closed string double field theory. In terms of undoubled component fields, it couples a usual Yang-Mills gauge field to an additional one-form field and also to the closed string background fields which consist of a dilaton, graviton and a two-form gauge field. Our resulting action resembles a twisted Yang-Mills action.     

BRST quantization in the Siegel gauge

From a formal generalization to N copies of the free open string field theory BRST-quantized in the Siegel gauge we reproduce the BRST quantization of the free closed bosonic string field theory and obtain the one of massless higher spin field theories.     

N = 4 Yang-Mills theory in terms of N = 3 and N = 2 light-cone superfields

The N = 4 Yang-Mills theory is truncated to an N = 3 Yang-Mills theory and to an N = 2 Yang-Mills theory coupled to an N = 2 Wess-Zumino field. The whole procedure is performed in the light-cone gauge. It is then shown that these theories are unique even if we only insist on N = 3 or N = 2 supersymmetry respectively. Finally we show in detail how the introduction of the fermionic Wess-Zumino field renders the one-loop self-energy finite.     

Resummation in hot field theories

There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the perturbative expansion. This effective expansion which is due to Braaten and Pisarski, can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of g. However, it turns out that the weak-coupling expansion for thermodynamic quantities are useless unless the coupling constant is very small. We critically discuss various ways of reorganizing the perturbative series for thermal field theories in order to improve its convergence. These include screened perturbation theory (SPT), hard-thermal-loop perturbation theory, the Φ-derivable approach, dimensionally reduced (DR) SPT, and the DR Φ-derivable approach.     

Mean field solution to the intermediate valence problem

We introduce a mean field theory of IV systems, corresponding to the limit of infinite degeneracy N = 2j + 1. For a single RE impurity we correct it to next order in 1/N. For the lattice the mean field theory for the first time leads to an ab initio derivation of a renormalized band structure.     

External gravitational interactions in quantum field theory

We consider the renormalization of Green's functions of λφ⁴ quantum field theory in an external gravitational field specified by the metric tensor g^μν(y). Green's functions Γ^(n,3) describing the interaction of j scalar particles to arbitrary order n in the gravitational field are shown to be made finite by the standard renormalizations of the flatspace theory and a renormalization of the coefficient of the improvement term in the action functional. These results in φ⁴ theory can be extended to all renormalizable field theories.     

Spontaneous symmetry breaking in Reggeon field theory

We consider a Reggeon field theory when the bare or input Regge intercept α_O is greater than one. This corresponds to a negative mass squared term in conventional field theory and allows for a spontaneous symmetry break-down. A theory with Regge intercept at one emerges, restoring the Froissart bound by t-channel considerations alone. In our elementary example the resulting bare trajectory is nearly of the square root variety familiar from s-channel eikonalization of models which violate the Froissart bound.