Fusion Rules in N=1 Superconformal Minimal Models

The generalization to N=1 superconformal minimal models of the relation between the modular transformation matrix and the fusion rules in rational conformal field theories, the Verlinde theorem, is shown to provide complete information about the fusion rules, including their fermionic parity. The results for the superconformal Tricritical Ising and Ashkin-Teller models agree with the known rational conformal formulation. The Coulomb gas description of correlation functions in the Ramond sector of N=1 minimal models is also discussed and a previous formulation is completed.Comment: 13 pages, latex, to appear in Phys. Lett.

Scalar Field Theory in the AdS/CFT Correspondence Revisited

We consider the role of boundary conditions in the $AdS_{d+1}/CFT_{d}$ correspondence for the scalar field theory. Also a careful analysis of some limiting cases is presented. We study three possible types of boundary conditions, Dirichlet, Neumann and mixed. We compute the two-point functions of the conformal operators on the boundary for each type of boundary condition. We show how particular choices of the mass require different treatments. In the Dirichlet case we find that there is no double zero in the two-point function of the operator with conformal dimension $\frac{d}{2}$. The Neumann case leads to new normalizations for the boundary two-point functions. In the massless case we show that the conformal dimension of the boundary conformal operator is precisely the unitarity bound for scalar operators. We find a one-parameter family of boundary conditions in the mixed case. There are again new normalizations for the boundary two-point functions. For a particular choice of the mixed boundary condition and with the mass squared in the range $-d^2/4<m^2<-d^2/4+1$ the boundary operator has conformal dimension comprised in the interval $[\frac{d-2}{2}, \frac{d}{2}]$. For mass squared $m^2>-d^2/4+1$ the same choice of mixed boundary condition leads to a boundary operator whose conformal dimension is the unitarity bound.Comment: 22 pages, LaTeX, minor errors corrected, Conclusions and one reference added, final version to be published in Nucl. Phys.

Multi-Trace Operators and the Generalized AdS/CFT Prescription

We show that multi-trace interactions can be consistently incorporated into an extended AdS/CFT prescription involving the inclusion of generalized boundary conditions and a modified Legendre transform prescription. We find new and consistent results by considering a self-contained formulation which relates the quantization of the bulk theory to the AdS/CFT correspondence and the perturbation at the boundary by double-trace interactions. We show that there exist particular double-trace perturbations for which irregular modes are allowed to propagate as well as the regular ones. We perform a detailed analysis of many different possible situations, for both minimally and non-minimally coupled cases. In all situations, we make use of a new constraint which is found by requiring consistence. In the particular non-minimally coupled case, the natural extension of the Gibbons-Hawking surface term is generated.Comment: 27 pages, LaTeX, v.2:minor changes, v.3:comments added, v.4:several new results, discussions, references and a section of Conclusions added. Previous results unchanged, v.5: minor changes. Final version to be published in Phys.Rev.

Four Point Functions in the SL(2,R) WZW Model

We consider winding conserving four point functions in the SL(2,R) WZW model for states in arbitrary spectral flow sectors. We compute the leading order contribution to the expansion of the amplitudes in powers of the cross ratio of the four points on the worldsheet, both in the m- and x-basis, with at least one state in the spectral flow image of the highest weight discrete representation. We also perform certain consistency check on the winding conserving three point functions.Comment: 15 pages, Late

Winding Strings in AdS_3

Correlation functions of one unit spectral flowed states in string theory on AdS_3 are considered. We present the modified Knizhnik-Zamolodchikov and null vector equations to be satisfied by amplitudes containing states in winding sector one and study their solution corresponding to the four point function including one w=1 field. We compute the three point function involving two one unit spectral flowed operators and find expressions for amplitudes of three w=1 states satisfying certain particular relations among the spins of the fields. Several consistency checks are performed.Comment: 35 pages. v2. Important additions: one more author, complete results for the 3-point function with two w=1 states and new section with computation of 4-point function with one w=1 state. Acknowledgments and references modifie

Chern-Simons Theories in the AdS/CFT Correspondence

We consider the AdS/CFT correspondence for theories with a Chern-Simons term in three dimensions. We find the two-point functions of the boundary conformal field theories for the Proca-Chern-Simons theory and the Self-Dual model. We also discuss particular limits where we find the two-point function of the boundary conformal field theory for the Maxwell-Chern-Simons theory. In particular our results are consistent with the equivalence between the Maxwell-Chern-Simons theory and the Self-Dual model.Comment: 14 pages, Latex, bulk solutions corrected and boundary terms derived from the variational principle, minor corrections, version to be publishe

Bound States in the AdS/CFT Correspondence

We consider a massive scalar field theory in anti-de Sitter space, in both minimally and non-minimally coupled cases. We introduce a relevant double-trace perturbation at the boundary, by carefully identifying the correct source and generating functional for the corresponding conformal operator. We show that such relevant double-trace perturbation introduces changes in the coefficients in the boundary terms of the action, which in turn govern the existence of a bound state in the bulk. For instance, we show that the usual action, containing no additional boundary terms, gives rise to a bound state, which can be avoided only through the addition of a proper boundary term. Another notorious example is that of a conformally coupled scalar field, supplemented by a Gibbons-Hawking term, for which there is no associated bound state. In general, in both minimally and non-minimally coupled cases, we explicitly compute the boundary terms which give rise to a bound state, and which ones do not. In the non-minimally coupled case, and when the action is supplemented by a Gibbons-Hawking term, this also fixes allowed values of the coupling coefficient to the metric. We interpret our results as the fact that the requirement to satisfy the Breitenlohner-Freedman bound does not suffice to prevent tachyonic behavior from existing in the bulk, as it must be supplemented by additional conditions on the coefficients in the boundary terms of the action.Comment: 32 pages, Latex. v2: added comments and clarifications, minor changes. v3: corrected wrong result in the non-minimally coupled case, added reference, minor changes. v4: Added new results and discussions, parts of the paper are rewritten. Final version to be published in Phys.Rev.

A Note on Scalar Field Theory in AdS_3/CFT_2

We consider a scalar field theory in AdS_{d+1}, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions \Delta_{-} and \Delta_{+}, respectively, where \Delta_{\pm} are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d=2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS_3/CFT_2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results.Comment: 24 pages. v2: added minor clarification. v3: added several comments and discussions, abstract sligthly changed. Version to be publishe

Duality between Noncommutative Yang-Mills-Chern-Simons and Non-Abelian Self-Dual Models

By introducing an appropriate parent action and considering a perturbative approach, we establish, up to fourth order terms in the field and for the full range of the coupling constant, the equivalence between the noncommutative Yang-Mills-Chern-Simons theory and the noncommutative, non-Abelian Self-Dual model. In doing this, we consider two different approaches by using both the Moyal star-product and the Seiberg-Witten map.Comment: 6 pages, LaTeX. v2 minor changes. v3 substantial additions, including a new section discussing the Seiberg-Witten map. v4 references and comments added. Final version to be published in Phys. Lett.