34 research outputs found
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 ( and ), 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 and and show that in the presence of the non-coset degrees of freedom the important property of the Lax connection to be -invariant persists. In the case of the superstring we also
study the string instanton wrapping a non-trivial two-cycle in and find that it has twelve fermionic zero modes associated with of the supersymmetry of the background, thus manifesting that this exact topologically non-trivial classical solution is BPS.L'argomento di questa tesi sono le Teorie di Superstringa su spazi Anti de Sitter che non hanno supersimmetria massimale ( e ), 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 e e mostriamo che in presenza dei gradi di libertà non-coset la -invarianza persiste. Nel caso della superstringa in studiamo anche l'istantone di stringa che si avvolge su di un ciclo non triviale in e troviamo che ha dodici zero modi fermionici associati con delle supersimmetrie dello spazio, quindi che questa soluzione classica, esatta e topologicamente non-banale è 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 () correspondences, with a peculiar attention to the cases in which the GS superstring theory is not fully described by a supercoset sigma model