Howard J. Schnitzer

A GKO Construction Based on a Path Integral Formulation of Gauged Wess-Zumino-Witten Actions

Abstract A path integral formulation of G/H conformal theories is presented, based on gauged Wess-Zumino-Witten actions. The conformal charge of the model is c = c G − c H , exactly as in the GKO construction. Ghost modes appear in the formalism as a result of gauge fixing. As a consequence, the holomorphic stress-tensor T ( z ) obtained in our construction has ghost contributions. We find T ( z )= T G − T H only for matrix elements of physical states which are also ghost free.

BRST Quantization of the Gauged WZW Action and Coset Conformal Field Theories

The relation of the gauged Wess-Zumino-Witten models describing G/H conformal field theories and the GKO construction is investigated in the BRST framework. A nilpotent operator Q is constructed and the physical spectrum and unitarity of the theory is analyzed. When H is the Cartan subalgebra of G the BRST invariant current operators (the physical currents) are shown to be the parafermionic operators.

Matrix model approach to the Script N = 2 U(N) gauge theory with matter in the fundamental representation

We use matrix model technology to study the = 2 U(N) gauge theory with Nf massive hypermultiplets in the fundamental representation. We perform a completely perturbative calculation of the periods ai and the prepotential (a) up to the first instanton level, finding agreement with previous results in the literature. We also derive the Seiberg-Witten curve and differential from the large-M solution of the matrix model. We show that the two cases Nf < N and N ≤ Nf < 2N can be treated simultaneously.

Virtual effects of excited quarks as probes of a possible new hardonic mass scale

Abstract The effects of spin - 3 2 excited quarks are considered as probes of a possible new hadronic mass-scale Λ. A specific model is developed which describes virtual spin - 3 2 quarks of mass of O(Λ). Induced effects, which are corrections to the standard SU(2) × U(1) electroweak model, include right-handed charged currents and flavor changing neutral currents. A model-independent classification of all SU(3) × SU(2) × U(1) invariant quark operators of dimension six or less is also presented. Ambiguities in converting this analysis and existing experiments to a definitive lower-bound for Λ are discussed. It is found, depending on the strength of certain Higgs couplings and the underlying global flavor symmetries in the absence of Higgs couplings, that a lower bound as small as Λ > 500 GeV or as large as Λ > 100 TeV is possible.

The N=2 U(N) gauge theory prepotential and periods from a perturbative matrix model calculation

Abstract We perform a completely perturbative matrix model calculation of the physical low-energy quantities of the N =2 U(N) gauge theory. Within the matrix model framework we propose a perturbative definition of the periods ai in terms of certain tadpole diagrams, and check our conjecture up to first order in the gauge theory instanton expansion. The prescription does not require knowledge of the Seiberg–Witten differential or curve. We also compute the N =2 prepotential F (a) perturbatively up to the first-instanton level, finding agreement with the known result.

Higgs-regularized three-loop four-gluon amplitude in \mathcal{N} = 4 SYM: exponentiation and Regge limits

We compute the three-loop contribution to the

Group-level duality in WZW models and Chern-Simons theory☆

\mathcal{N} = 4

A path integral construction of superconformal field theories from a gauged supersymmetric Wess-Zumino-Witten action

supersymmetric Yang-Mills planar four-gluon amplitude using the recently-proposed Higgs IR regulator of Alday, Henn, Plefka, and Schuster. In particular, we test the proposed exponential ansatz for the four-gluon amplitude that is the analog of the BDS ansatz in dimensional regularization. By evaluating our results at a number of kinematic points, and also in several kinematic limits, we establish the validity of this ansatz at the three-loop level.We also examine the Regge limit of the planar four-gluon amplitude using several different IR regulators: dimensional regularization, Higgs regularization, and a cutoff regularization. In the latter two schemes, it is shown that the leading logarithmic (LL) behavior of the amplitudes, and therefore the lowest-order approximation to the gluon Regge trajectory, can be correctly obtained from the ladder approximation of the sum of diagrams. In dimensional regularization, on the other hand, there is no single dominant set of diagrams in the LL approximation. We also compute the NLL and NNLL behavior of the L-loop ladder diagram using Higgs regularization.

Group-level duality of WZW fusion coefficients and Chern-Simons link observables

Abstract We exhibit a duality of primary fields, conformal dimensions, braid matrices, and modular transformation matrix elements S0,λ/S0,0 (so also Weyl characters) for sequences of dual pairs (SU (N)K, SU(K)N), (SO(N)K, (SO(N)K, SO(K)N) and Sp(N)K, Sp(K)N. As a consequence an analogous duality of Chern-Simons skein relations and Wilson line observables is uncovered.

The soft-pion skyrmion lagrangian and strong CP-violation

Abstract A path integral construction of superconformal field theories is presented based on gauged supersymmetric Wess-Zumino-Witten actions. The conformal charge of the model is identical to that of a GKO construction. Ghost modes appear in the formalism as a result of gauge fixing. As a consequence, the holomorphic stress-tensor T ( z ) and superconformal generator G ( z ) obtained in the construction have ghost contributions. Weak operator first-class constraints restrict the theory to physical states which satisfy the constraints. The superconformal algebra closes when evaluated between ghost-free physical states.