On the Spectrum of Superspheres

Sigma models on coset superspaces, such as odd dimensional superspheres, play an important role in physics and in particular the AdS/CFT correspondence. In this work we apply recent general results on the spectrum of coset space models and on supergroup WZNW models to study the conformal sigma model with target space S^{3|2}. We construct its vertex operators and provide explicit formulas for their anomalous dimensions, at least to leading order in the sigma model coupling. The results are used to revisit a non-perturbative duality between the supersphere and the OSP(4|2) Gross-Neveu model that was conjectured by Candu and Saleur. With the help of powerful all-loop results for 1/2 BPS operators in the Gross-Neveu model we are able to recover the entire zero mode spectrum of the sigma model at a certain finite value of the Gross-Neveu coupling. In addition, we argue that the sigma model constraints and equations of motion are implemented correctly in the dual Gross-Neveu description. On the other hand, high(er) gradient operators of the sigma model are not all accounted for. It is possible that this discrepancy is related to an instability from high gradient operators that has previously been observed in the context of Anderson localization

Spectra of Sigma Models on Semi-Symmetric Spaces

Sigma models on semi-symmetric spaces provide the central building block for string theories on AdS backgrounds. Under certain conditions on the global supersymmetry group they can be made one-loop conformal by adding an appropriate fermionic Wess-Zumino term. We determine the full one-loop dilation operator of the theory. It involves an interesting new XXZ-like interaction term. Eigenvalues of our dilation operator, i.e. the one-loop anomalous dimensions, are computed for a few examples

High-Gradient Operators in the psl(2|2) Gross-Neveu Model

It has been observed more than 25 years ago that sigma model perturbation theory suffers from strongly RG-relevant high-gradient operators. The phenomenon was first seen in 1-loop calculations for the O(N) vector model and it is known to persist at least to two loops. More recently, Ryu et al. suggested that a certain deformation of the psl(N|N) WZNW-model at level k = 1, or equivalently the psl(N|N) Gross-Neveu model, could be free of RG-relevant high-gradient operators and they tested their suggestion to leading order in perturbation theory. In this note we establish the absence of strongly RG-relevant high-gradient operators in the psl(2|2) Gross-Neveu model to all loops. In addition, we determine the spectrum for a large subsector of the model at infinite coupling and observe that all scaling weights become half-integer. Evidence for a conjectured relation with the CP^1|2 sigma model is not found.Comment: 14 page

An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction

We introduce a series of articles reviewing various aspects of integrable models relevant to the AdS/CFT correspondence. Topics covered in these reviews are: classical integrability, Yangian symmetry, factorized scattering, the Bethe ansatz, the thermodynamic Bethe ansatz, and integrable structures in (conformal) quantum field theory. In the present article we highlight how these concepts have found application in AdS/CFT, and provide a brief overview of the material contained in this series.Comment: v2, published versio

More on integrable structures of superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds

In this paper we continue the study, initiated in arXiv:1009.3498 and arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum contains non-supercoset worldsheet degrees of freedom corresponding to broken supersymmetries in the bulk. We derive an explicit expression, to all orders in the coset fermions and to second order in the non-coset fermions, which extends the supercoset Lax connection in these backgrounds with terms depending on the non-coset fermions. An important property of the obtained form of the Lax connection is that it is invariant under Z_4-transformations of the superisometry generators and the spectral parameter. This demonstrates that the contribution of the non-coset fermions does not spoil the Z_4-symmetry of the super-coset Lax connection which is of crucial importance for the application of Bethe-ansatz techniques. The expressions describing the AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superstring sigma--models and their Lax connections have a very similar form. This is because their amount of target-space supersymmetries complement each other to 32=24+8, the maximal number of 10d type II supersymmetries. As a byproduct, this similarity has allowed us to obtain the form of the geometry of the complete type IIA AdS(2) x S(2) x T(6) superspace to all orders in the coset fermions and to the second order in the non-coset ones.Comment: 28 pages; v2: References adde

Superstring Theories on non-maximally supersymmetric AdS backgrounds

The subject of this thesis is Superstring Theories on Anti de Sitter backgrounds that do not have maximal supersymmetry ($AdS_4\times CP^3$ and $AdS_2\times S^2\times T^6$), a feature that introduces complications in studying these theories. In particular, in the non-maximally supersymmetric backgrounds the Green-Schwarz superstring is not fully described by a worldsheet sigma model on a corresponding supercoset space, since it has extra (non-coset) fermionic degrees of freedom associated with the broken supersymmetries. We concentrate on the study of the integrability of these theories with the aim to reveal how the non-coset fermionic modes enter into and deform the integrable structure of these string theories. We construct various (gauge-related) forms of the zero-curvature Lax connecton for the superstrings in $AdS_4\times CP^3$ and $AdS_2\times S^2\times T^6$ and show that in the presence of the non-coset degrees of freedom the important property of the Lax connection to be $\mathbb Z_4$-invariant persists. In the case of the $AdS_4\times CP^3$ superstring we also study the string instanton wrapping a non-trivial two-cycle in $CP^3$ and find that it has twelve fermionic zero modes associated with $1/2$ of the supersymmetry of the background, thus manifesting that this exact topologically non-trivial classical solution is $1/2$ BPS.L'argomento di questa tesi sono le Teorie di Superstringa su spazi Anti de Sitter che non hanno supersimmetria massimale ($AdS_4\times CP^3$ e $AdS_2\times S^2\times T^6$), una caretteristica che introduce molte complicazioni nello studio delle teorie stesse. In particolare, in spazi non massimamente supersimmetrici la superstringa di Green-Schwarz non è completamente descritta da un modello sigma di worldsheet sul corrispondente spazio di coset, dato che possiede ulteriori gradi di libertà fermionici (non-coset), associati alle supersimmetrie rotte. Ci concentriamo sullo studio dell'Integrabilità di queste teorie con l'obbiettivo di scoprire come i modi ferionici di non-coset entrino in e deformino la struttura integrabile di queste teorie di stringa. Costruiamo varie forme (collegate da trasformazioni di gauge) di connessioni di Lax a curvatura zero per la stringa in $AdS_4\times CP^3$ e $AdS_2\times S^2\times T^6$ e mostriamo che in presenza dei gradi di libertà non-coset la $\mathbb Z_4$-invarianza persiste. Nel caso della superstringa in $AdS_4\times CP^3$ studiamo anche l'istantone di stringa che si avvolge su di un ciclo non triviale in $CP^3$ e troviamo che ha dodici zero modi fermionici associati con $1/2$ delle supersimmetrie dello spazio, quindi che questa soluzione classica, esatta e topologicamente non-banale è $1/2$ BPS

Classical Integrability in AdS/CFT

Integrability based techniques are widely used to study AdS/CFT correspondences, for this reason to show Integrability of Superstring Theories that have a gauge dual is peculiarly interesting. I will focus on Classical Integrability of Superstring Theories on non maximally supersymmetric AdS backgrounds, that are involved in $AdS_n/CFT_{n−1}$ ($n=2,3,4$) correspondences, with a peculiar attention to the cases in which the GS superstring theory is not fully described by a supercoset sigma model