New coherent states and modified heat equations

We clarify the relations between certain new coherent states for loop quantum gravity and the analytically continued heat kernel coherent states, highlighting the underlying general construction, the presence of a modified heat equation as well as the way in which the properties of the heat kernels are automatically inherited by these new states.Comment: 7 page

Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4

We establish features of so-called Yangian secret symmetries for AdS3 type IIB superstring backgrounds thus verifying the persistence of such symmetries to this new instance of the AdS/CFT correspondence. Specifically, we find two a priori different classes of secret symmetry generators. One class of generators, anticipated from the previous literature, is more naturally embedded in the algebra governing the integrable scattering problem. The other class of generators is more elusive, and somewhat closer in its form to its higher-dimensional AdS5 counterpart. All of these symmetries respect left-right crossing. In addition, by considering the interplay between left and right representations, we gain a new perspective on the AdS5 case. We also study the RTT-realisation of the Yangian in AdS3 backgrounds thus establishing a new incarnation of the Beisert-de Leeuw construction.Comment: v2: 21 pages, clarifications added, typos fixed, published versio

Twisted Index on Hyperbolic Four-Manifolds

We introduce the topologically twisted index for four-dimensional $\mathcal N=1$ gauge theories quantized on ${\rm AdS}_2 \times S^1$. We compute the index by applying supersymmetric localization to partition functions of vector and chiral multiplets on ${\rm AdS}_2 \times T^2$, with and without a boundary: in both instances we classify normalizability and boundary conditions for gauge, matter and ghost fields. The index is twisted as the dynamical fields are coupled to a R-symmetry background 1-form with non-trivial exterior derivative and proportional to the spin connection. After regularization the index is written in terms of elliptic gamma functions, reminiscent of four-dimensional holomorphic blocks, and crucially depends on the R-charge.Comment: 22 page

The Spindle Index from Localization

We present a new supersymmetric index for three-dimensional ${\cal N}=2$ gauge theories defined on $\Sigma \times S^1$, where $\Sigma$ is a spindle, with twist or anti-twist for the $R$-symmetry background gauge field. We start examining general supersymmetric backgrounds of Euclidean new minimal supergravity admitting two Killing spinors of opposite $R$-charges. We then focus on $\Sigma \times S^1$ and demostrate how to realise twist and anti-twist. We compute the supersymmetric partition functions on such backgrounds via localization and show that these are captured by a general formula, depending on the type of twist, which unifies and generalises the superconformal and topologically twisted indices.Comment: 5 pages, v2: minor changes, eq. (40) adde

T-Duality of Green-Schwarz Superstrings on AdS(d) x S(d) x M(10-2d)

We verify the self-duality of Green-Schwarz supercoset sigma models on AdS$_d \times S^d$ backgrounds (d=2,3,5) under combined bosonic and fermionic T-dualities without gauge fixing kappa symmetry. We also prove this property for superstrings on AdS$_d \times S^d \times S^d$ (d=2,3) described by supercoset sigma models with the isometries governed by the exceptional Lie supergroups $D(2,1;\alpha)$ (d=2) and $D(2,1;\alpha)\times D(2,1;\alpha)$ (d=3), which requires an additional T-dualisation along one of the spheres. Then, by taking into account the contribution of non-supercoset fermionic modes (up to the second order), we provide evidence for the T-self-duality of the complete type IIA and IIB Green-Schwarz superstring theory on AdS$_d\times S^d \times T^{10-2d}$ (d=2,3) backgrounds with Ramond-Ramond fluxes. Finally, applying the Buscher-like rules to T-dualising supergravity fields, we prove the T-self-duality of the whole class of the AdS$_d\times S^d \times M^{10-2d}$ superbackgrounds with Ramond-Ramond fluxes in the context of supergravity.Comment: v2: 57 pages, 1 figure, typos fixed and clarifications added, version to appear in JHE

Dualities and integrability in low dimensional AdS/CFT.

Scientific abstract In this dissertation we perform a series of study concerning dualities and integrability properties underlying the AdS3/CFT2 and AdS2/CFT1 correspondences. These are particularly interesting because symmetry do not constrain the dynamics of AdS3 and AdS3 superstrings in the same way as in the higher dimensional instances of AdS/CFT, allowing for novel phenomena such as the presence of massless worldsheet modes or non-coset fermions. We will investigate the self-duality of Green–Schwarz supercoset sigma models on AdSd⇥Sd⇥Sd (d = 2, 3), whose isometry supergroups are (d − 1) copies of the exceptional Lie supergroup D(2, 1; ↵). Our main finding is that additional complex T-dualities along one of the spheres Sd are needed to map the superstring action to itself. Importantly, this proves dual superconformal symmetry of their CFT duals via AdS/CFT. Dual superconformal symmetry is strictly related to integrability, which we study in depth for both AdS3 and AdS2 superstrings. Indeed, we will derive the exact S-matrix conjectured to be related to the massive modes of type IIB AdS2 ⇥ S2 ⇥ T6 superstrings. This S-matrix is psuc(1|1) invariant and it was found to be in perfect agreement with the tree-level result following from string perturbation theory. We also unveil the Yangian algebra ensuring the integrability of the AdS2⇥S2⇥T6 superstring in the planar limit, Y[psu(1|1)c], as well as its secret symmetries. By using the RTT realisation, we provide two di↵erent representations of the Hopf algebra: one is reminiscent of the Yangian underlying AdS5/CFT4, but it is not of evaluation type. The other representation, obtained from co-commutativity, is instead of evaluation type. We explore two limits of the S-matrix for AdS2/CFT1: one is the classical r-matrix, which is the first non-trivial order in the 1/g expansion, with g being the e↵ective tension in the AdS2 ⇥ S2 ⇥ T6 superstring action. In this limit, corresponding to classical strings, we found that secret symmetries not only are present, but also essential to formulate the classical rmatrix in a universal, representation independent form. On the other hand, the limit g ! 0, corresponding to the weakly coupled CFT1, shows that the dual integrable model is described by an e↵ective theory of free fermions on a periodic spin-chain if g = 0, while one obtains a non-trivial spin chain of XYZ type if g 6= 0. Finally, we investigate Yangian and secret symmetries for AdS3 type IIB superstring backgrounds, verifying the persistence of such structures in AdS3/CFT2. Especially, we find that the antipode map, related to crossing symmetry, exchanges in a non-trivial way left and right generators of Y[psu(1|1)2c], the Yangian underlying the integrability of AdS3 superstrings. Keywords and AMS Classification Codes

Supersymmetric localization of refined chiral multiplets on topologically twisted H-2 x S-1

We derive the partition function of an N = 2 chiral multiplet on topologically twisted H-2 x S-1. The chiral multiplet is coupled to a background vector multiplet encoding a real mass deformation. We consider an H-2 x S-1 metric containing two parameters: one is the S-1 radius, while the other gives a fugacity q for the angular momentum on H-2. The computation is carried out by means of supersymmetric localization, which provides a finite answer written in terms of q-Pochammer symbols and multiple Zeta functions. Especially, the partition function of normalizable fields reproduces three-dimensional holomorphic blocks. (C) 2019 The Author(s). Published by Elsevier B.V