Free Field Realization Research Articles

Type 0A matrix model of a black hole, integrability, and holography

We investigate a deformed matrix model of type 0A theory related to supersymmetric Witten's black hole in two-dimensions, generalization of bosonic model suggested by Kazakov et. al. We find a free field realization of the partition function of the matrix model, which includes Ramond-Ramond perturbations in the type 0A theory. In a simple case, the partition function is factorized into two determinants, which are given by $\tau$ function of an integrable system. We work out the genus expansion of the partition function. Holographic relation with the supersymmetric Witten's black hole is checked by Wilson line computation. Corresponding partition function of the matrix model exhibits a singular behavior, which is interpreted as the point of enhanced ${\cal N}=2$ worldsheet supersymmetry. Interesting relation of the deformed matrix model and topological string on a $Z_2$ orbifold of conifold is found.

Free field realization of superstring theory on AdS3

The Coulomb gas representation of expectation values in SU(2) conformal field theory developed by Dotsenko is extended to the SL(2,R) WZW model and applied to bosonic string theory on AdS3 and to Type II superstrings on AdS3 x N. The spectral flow symmetry is included in the free field realization of vertex operators creating superstring states of both Ramond and Neveu-Schwarz sectors. Conjugate representations for these operators are constructed and a background charge prescription is designed to compute correlation functions. Two and three point functions of bosonic and fermionic string states in arbitrary winding sectors are calculated. Scattering amplitudes that violate winding number conservation are also discussed.

The Drinfeld realization of the elliptic quantum group Bq,λ(A2(2))

We construct a realization of the L-operator satisfying the RLL-relation of the face-type elliptic quantum group Bq,λ(A2(2)). The construction is based on the elliptic analog of the Drinfeld currents of Uq(A2(2)), which forms the elliptic algebra Uq,p(A2(2)). We give a realization of the elliptic currents E(z), F(z), and K(z) as a tensor product of the Drinfeld currents of Uq(A2(2)) and a Heisenberg algebra. In the level-one representation, we also give a free field realization of the elliptic currents. Applying these results, we derive a free field realization of the Uq,p(A2(2))-analog of the Bq,λ(A2(2))-intertwining operators. The resultant operators coincide with those of the vertex operators in the dilute AL model, which is known to be a RSOS restriction of the A2(2) face model.

Quantum reduction and representation theory of superconformal algebras

We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all superconformal algebras.

Remarks on free field realization of SL(2,R)/U(1) U(1) WZNW model

Free field representations of vertex algebra in SL(2,R)/U(1) x U(1) WZNW model are constructed by considering a twisted version of the Bershadsky-Kutasov free field description of discrete states in the two-dimensional black hole CFT. These correspond to conjugate representations describing primary states in the model on SL(2,R)/U(1) x U(1). A particular evaluation of these leads to identities due to the spectral flow symmetry of sl(2)_k algebra. The computation of correlation functions is discussed and, as an application, these are compared with analogous results known for the sine-Liouville theory. Exact agreement is observed between both analytic structures.

DDF and Pohlmeyer invariants of (super)string

We show how the Pohlmeyer invariants of the bosonic string are expressible in terms of DDF invariants. Quantization of the DDF observables in the usual way yields a consistent quantization of the algebra of Pohlmeyer invariants. Furthermore it becomes straightforward to generalize the Pohlmeyer invariants to the superstring as well as to all backgrounds which allow a free field realization of the worldsheet theory.

FREE FIELD APPROACH TO D-BRANES IN N=2 SUPERCONFORMAL MINIMAL MODELS

The approach to construction of D-branes in the N=2 superconformal minimal models based on a free-field realization of the N=2 super-Virasoro algebra unitary modules is represented.

Quantum reduction and representation theory of superconformal algebras

We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all superconformal algebras.

Strings in Gravimagnetic Fields

We provide a complete solution of closed strings propagating in Nappi-Witten space. Based on the analysis of geodesics we construct the coherent wavefunctions which approximate as closely as possible the classical trajectories. We then present a new free field realization of the current algebra using the γ,β ghost system. Finally we construct the quantum vertex operators, for the tachyon, by representing the wavefunctions in terms of the free fields. This allows us to compute the three- and four-point amplitudes, and propose the general result for N-point tachyon scattering amplitude.

Types of two-dimensionalN = 4 superconformal field theories

Various types ofN = 4 superconformal symmetries in two dimensions are considered. It is proposed that apart from the well-known cases ofSU (2)and SU(2) × SU(2) ×U (1), their Kac-Moody symmetry can also be SU(2) × (U (1))4. Operator product expansions for the last case are derived. A complete free field realization for the same is obtained

Explicit description of twisted Wakimoto realizations of affine Lie algebras

In a vertex algebraic framework, we present an explicit description of the twisted Wakimoto realizations of the affine Lie algebras in correspondence with an arbitrary finite order automorphism and a compatible integral gradation of a complex simple Lie algebra. This yields generalized free field realizations of the twisted and untwisted affine Lie algebras in any gradation. The free field form of the twisted Sugawara formula and examples are also exhibited.

Lie Subalgebras of Differential Operators on the Super Circle

We classify anti-involutions of Lie superalgebra \widehat{\mathcal{SD}} preserving the principal gradation, where \widehat{\mathcal{SD}} is the central extension of the Lie superalgebra of differential operators on the super circle S^{1\mid 1} . We clarify the relations between the corresponding subalgebras fixed by these anti-involutions and subalgebras of \widehat{gl}_{∞|∞} of types OSP and P . We obtain a criterion for an irreducible highest weight module over these subalgebras to be quasifinite and construct free field realizations of a distinguished class of these modules. We further establish dualities between them and certain finite-dimensional classical Lie groups on Fock spaces.

Free field construction of D-branes in N=2 superconformal minimal models

The construction of D-branes in N=2 superconformal minimal models based on free-field realization of N=2 super-Virasoro algebra unitary modules is represented.

Free boson formulation of boundary states inW3minimal models and the critical Potts model

We develop a Coulomb gas formalism for boundary conformal field theory having a $W$ symmetry and illustrate its operation using the three state Potts model. We find that there are free-field representations for six $W$ conserving boundary states, which yield the fixed and mixed physical boundary conditions, and two $W$ violating boundary states which yield the free and new boundary conditions. Other $W$ violating boundary states can be constructed but they decouple from the rest of the theory. Thus we have a complete free-field realization of the known boundary states of the three state Potts model. We then use the formalism to calculate boundary correlation functions in various cases. We find that the conformal blocks arising when the two point function of $\phi_{2,3}$ is calculated in the presence of free and new boundary conditions are indeed the last two solutions of the sixth order differential equation generated by the singular vector.

The Elliptic Algebra and the Drinfeld Realization of the Elliptic Quantum Group

By using the elliptic analogue of the Drinfeld currents in the elliptic algebra U_{q,p}(\hat{sl}_N), we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum group B_{q,\lambda}(\hat{sl}_N). For this purpose, we introduce a set of new currents K_j(v) (1\leq j\leq N) in U_{q,p}(\hat{sl}_N). As in the N=2 case, we find a structure of U_{q,p}(\hat{sl}_N) as a certain tensor product of B_{q,\lambda}(\hat{sl}_N) and a Heisenberg algebra. In the level-one representation, we give a free field realization of the currents in U_{q,p}(\hat{sl}_N). Using the coalgebra structure of B_{q,\lambda}(\hat{sl}_N) and the above tensor structure, we derive a free field realization of the U_{q,p}(\hat{sl}_N)-analogue of B_{q,\lambda}(\hat{sl}_N)-intertwining operators. The resultant operators coincide with those of the vertex operators in the A_{N-1}^{(1)}-type face model.

Onosp(2 2) conformal field theories

We study the conformal field theories corresponding to current superalgebras $osp(2|2)^{(1)}_k$ and $osp(2|2)^{(2)}_k$. We construct the free field realizations, screen currents and primary fields of these current superalgebras at general level $k$. All the results for $osp(2|2)^{(2)}_k$ are new, and the results for the primary fields of $osp(2|2)^{(1)}_k$ also seem to be new. Our results are expected to be useful in the supersymmetric approach to Gaussian disordered systems such as random bond Ising model and Dirac model.

Free-field realization of boundary states and boundary correlation functions of minimal models

We propose a general formalism to compute exact correlation functions for Cardy's boundary states. Using the free-field construction of boundary states and applying the Coulomb-gas technique, it is shown that charge neutrality conditions pick up particular linear combinations of conformal blocks. As an example we study the critical Ising model with free and fixed boundary conditions, and demonstrate that conventional results are reproduced. This formalism thus directly associates algebraically constructed boundary states with correlation functions which are in principle observable or numerically calculable.

From boundaries to conditions over superspace

N=1 and 2 superconformal boundary conditions are shown to be the consequence of a boundary on the worldsheet superspace with positive codimension in the anticommuting subspace. In addition to the well-known boundary conditions, I also find two new infinite series of N=2 boundary states. Their free field realizations are given. A self-contained development of 2d superspace leads to new perspectives on this subject.

Realizations of Conformal and Heisenberg Algebras in PP-wave-CFT Correspondence

We elaborate on the symmetry breaking pattern involved in the Penrose limit of $AdS_{d+1} \times S^{d+1}$ spacetimes and the corresponding limit of the CFT dual. For d=2 we examine in detail how the symmetries contract to products of rotation and Heisenberg algebras, both from the bulk and CFT points of view. Using a free field realization of these algebras acting on products of elementary fields of the CFT with SO(2) R charge +1, we show that this process of contraction restricts all the fields to a few low angular momentum modes and ensures that the field with R charge -1 does not appear. This provides an understanding of several important aspects of the proposal of Berenstein, Maldacena and Nastase. We also indicate how the contraction can be performed on correlation functions.

A(2)2 parafermions: a new conformal field theory

A new parafermionic algebra associated with the homogeneous space A (2) 2/ U(1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A (2) 2 parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy–momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a W-algebra type primary field with spin two.