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Ari Pakman

Publications and source records attributed to Ari Pakman.

35 records · Page 2Linked to original sources
arXiv2009

Diagrams for Symmetric Product Orbifolds

We develop a diagrammatic language for symmetric product orbifolds of two-dimensional conformal field theories. Correlation functions of twist operators are written as sums of diagrams: each diagram corresponds to a branched covering map from a surface where the fields are single-valued to the base sphere where twist operators are inserted. This diagrammatic language facilitates the study of the large N limit and makes more transparent the analogy between symmetric product orbifolds and free non-abelian gauge theories. We give a general algorithm to calculate the leading large N contribution to four-point correlators of twist fields.

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arXiv2009

Extremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds

We study correlation functions of single-cycle chiral operators in the symmetric product orbifold of N supersymmetric four-tori. Correlators of twist operators are evaluated on covering surfaces, generally of different genera, where fields are single-valued. We compute some simple four-point functions and study how the sum over inequivalent branched covering maps splits under OPEs. We then discuss extremal n-point correlators, i.e. correlators of n-1 chiral and one anti-chiral operators. They obey simple recursion relations involving numbers obtained from counting branched covering maps with particular properties. In most cases we are able to solve explicitly the recursion relations. Remarkably, extremal correlators turn out to be equal to Hurwitz numbers.

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arXiv2008

Topological Entanglement Entropy and Holography

We study the entanglement entropy in confining theories with gravity duals using the holographic prescription of Ryu and Takayanagi. The entanglement entropy between a region and its complement is proportional to the minimal area of a bulk hypersurface ending on their border. We consider a disk in 2+1 dimensions and a ball in 3+1 dimensions and find in both cases two types of bulk hypersurfaces with different topology, similar to the case of the slab geometry considered by Klebanov, Kutasov and Murugan. Depending on the value of the radius, one or the other type of hypersurfaces dominates the calculation of entanglement entropy. In 2+1 dimensions a useful measure of topological order of the ground state is the topological entanglement entropy, which is defined to be the constant term in the entanglement entropy of a disk in the limit of large radius. We compute this quantity and find that it vanishes for confining gauge theory, in accord with our expectations. In 3+1 dimensions the analogous quantity is shown to be generically nonzero and cutoff-dependent.

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arXiv2007

Spectral Flow in AdS(3)/CFT(2)

We study the spectral flowed sectors of the H3 WZW model in the context of the holographic duality between type IIB string theory in AdS(3)x S^3 x T^4 with NSNS flux and the symmetric product orbifold of T^4. We construct explicitly the physical vertex operators in the flowed sectors that belong to short representations of the superalgebra, thus completing the bulk-to-boundary dictionary for 1/2 BPS states. We perform a partial calculation of the string three-point functions of these operators. A complete calculation would require the three-point couplings of non-extremal flowed operators in the H3 WZW model, which are at present unavailable. In the unflowed sector, perfect agreement has recently been found between the bulk and boundary three-point functions of 1/2 BPS operators. Assuming that this agreement persists in the flowed sectors, we determine certain unknown three-point couplings in the H3 WZW model in terms of three-point couplings of affine descendants in the SU(2) WZW model.

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arXiv2007

Exact chiral ring of AdS(3)/CFT(2)

We carry out an exact worldsheet computation of tree level three-point correlators of chiral operators in string theory on AdS(3) x S^3 x T^4 with NS-NS flux. We present a simple representation for the string chiral operators in the coordinate basis of the dual boundary CFT. Striking cancelations occur between the three-point functions of the H3+ and the SU(2) WZW models which result in a simple factorized form for the final correlators. We show, by fixing a single free parameter in the H3+ WZW model, that the fusion rules and the structure constants of the N=2 chiral ring in the bulk are in precise agreement with earlier computations in the boundary CFT of the symmetric product of T^4 at the orbifold point in the large N limit.

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arXiv2007

Exact N=4 correlators of AdS(3)/CFT(2)

We extend to chiral N=4 operators the holographic agreement recently found between correlators of the symmetric orbifold of M^4 at large N and type IIB strings propagating in AdS(3) x S^3 x M^4, where M^4=T^4 or K3. We also present expressions for some bulk correlators not yet computed in the boundary.

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arXiv2006

FZZ Algebra

The duality between the Sine-Liouville conformal field theory and the two dimensional black hole is revisited by considering the two possible Sine-Liouville dressings together. We show that this choice is consistent with the structure of correlation functions, and that the OPE of the two dressings yields the black hole deformation operator. As an application of this approach, we investigate the role of higher winding perturbations in the context of c=1 strings, where we argue that they are related to higher-spin discrete states that generalize the 2d black hole operator.

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arXiv2006

FZZ Scattering

We study the duality between the two dimensional black hole and the sine-Liouville conformal field theories via exact operator quantization of a classical scattering problem. The ideas are first illustrated in Liouville theory, which is dual to itself under the interchange of the Liouville parameter b by 1/b. In both cases, a classical scattering problem does not determine uniquely the quantum reflection coefficient. The latter is only fixed by assuming that the dual scattering problem has the same reflection coefficient. We also discuss the relation of this approach to the method that exploits the parafermionic symmetry of the model to compute the reflection coefficient.

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arXiv2006

Liouville theory without an action

We show that the crossing symmetry of the four-point function in the Liouville conformal field theory on the sphere contains more information than what was hitherto considered. Under certain assumptions, it provides the special structure constants that were previously computed perturbatively and allows to solve the theory without using the Liouville interaction.

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arXiv2005

D-branes in Little String Theory

We analyze in detail the D-branes in the near-horizon limit of NS5-branes on a circle, the holographic dual of little string theory in a double scaling limit. We emphasize their geometry in the background of the NS5-branes and show the relation with D-branes in coset models. The exact one-point function giving the coupling of the closed string states with the D-branes and the spectrum of open strings is computed. Using these results, we analyze several aspects of Hanany-Witten setups, using exact CFT analysis. In particular we identify the open string spectrum on the D-branes stretched between NS5-branes which confirms the low-energy analysis in brane constructions, and that allows to go to higher energy scales. As an application we show the emergence of the beta-function of the N=2 gauge theory on D4-branes stretching between NS5-branes from the boundary states describing the D4-branes. We also speculate on the possibility of getting a matrix model description of little string theory from the effective theory on the D1-branes. By considering D3-branes orthogonal to the NS5-branes we find a CFT incarnation of the Hanany-Witten effect of anomalous creation of D-branes. Finally we give an brief description of some non-BPS D-branes.

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arXiv2005

D-branes in N=2 Liouville and its mirror

We study D-branes in the mirror pair N=2 Liouville / supersymmetric SL(2,R)/U(1) coset superconformal field theories. After revisiting the duality between the two models, we build D0, D1 and D2 branes, on the basis of the boundary state construction for the Euclidean AdS(3) conformal field theory. We also construct D0-branes in an orbifold that rotates the angular direction of the cigar. We show how the poles of correlators associated to localized states and bulk interactions naturally decouple in the one-point functions of localized and extended branes. We stress the role played in the analysis of D-brane spectra by primaries in SL(2,R)/U(1) which are descendents of the parent theory.

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arXiv2004

The partition function of the supersymmetric two-dimensional black hole and little string theory

We compute the partition function of the supersymmetric two-dimensional Euclidean black hole geometry described by the SL(2,R)/U(1) superconformal field theory. We decompose the result in terms of characters of the N=2 superconformal symmetry. We point out puzzling sectors of states besides finding expected discrete and continuous contributions to the partition function. By adding an N=2 minimal model factor of the correct central charge and projecting on integral N=2 charges we compute the partition function of the background dual to little string theory in a double scaling limit. We show the precise correspondence between this theory and the background for NS5-branes on a circle, due to an exact description of the background as a null gauging of SL(2,R) x SU(2). Finally, we discuss the interplay between GSO projection and target space geometry.

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arXiv2004

Extended SL(2,R)/U(1) characters, or modular properties of a simple non-rational conformal field theory

We define extended SL(2,R)/U(1) characters which include a sum over winding sectors. By embedding these characters into similarly extended characters of N=2 algebras, we show that they have nice modular transformation properties. We calculate the modular matrices of this simple but non-trivial non-rational conformal field theory explicitly . As a result, we show that discrete SL(2,R) representations mix with continuous SL(2,R) representations under modular transformations in the coset conformal field theory. We comment upon the significance of our results for a general theory of non-rational conformal field theories.

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arXiv2003

Type 0 Strings in a 2-d Black Hole

We study some aspects of type 0 strings propagating in the two dimensional black hole geometry, corresponding to the exact SL(2)/U(1) SCFT background.

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arXiv2003

BRST Quantization of String Theory in AdS(3)

We study the BRST quantization of bosonic and NSR strings propagating in AdS(3) x N backgrounds. The no-ghost theorem is proved using the Frenkel-Garland-Zuckerman method. Regular and spectrally-flowed representations of affine SL(2,R) appear on an equal footing. Possible generalizations to related curved backgrounds are discussed.

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arXiv2003

More on Superstrings in AdS(3) x N

We study superstring theories on AdS(3) x N backgrounds yielding N=2,3,4 extended superconformal symmetries in the dual boundary CFT. In each case the necessary constraints on the internal worldsheet theory N are found.

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