### J H E P12(2011)027

, 2011

"... Abstract: When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N = 2 string vacua and the Coulomb branch of rigid N = 2 gauge theories on R3 × S1 are strikingly similar and, to a large extent, dictated by consistency with wall-crossing. We elucidate this similar ..."

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Abstract: When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N = 2 string vacua and the Coulomb branch of rigid N = 2 gauge theories on R3 × S1 are strikingly similar and, to a large extent, dictated by consistency with wall-crossing. We elucidate this similarity by showing that these two spaces are related under a general duality between, on one hand, quaternion-Kähler manifolds with a quaternionic isometry and, on the other hand, hyperkähler manifolds with a rotational isometry, equipped with a canonical hyperholomorphic circle bundle and a connection. We show that the transition functions of the hyperholomorphic circle bundle relevant for the hypermultiplet moduli space are given by the Rogers dilogarithm function, and that consistency across walls of marginal stability is ensured by the motivic wall-crossing formula of Kontsevich and Soibelman. We illustrate the construction on some simple examples of wall-crossing related to cluster algebras for rank 2 Dynkin quivers. In an appendix we also provide a detailed discussion on the general relation between wall-crossing and cluster algebras.

### arXiv:1104.2474v2 [hep-th] 6 Jul 2011

"... Abstract. This review is meant to be an account of the properties of the infinitedimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a concise anthology of basic facts concerning Yangians ..."

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Abstract. This review is meant to be an account of the properties of the infinitedimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a concise anthology of basic facts concerning Yangians and integrable systems, and to store a series of remarks, observations and proofs the author has collected in a fiveyear span of research on the subject. We hope this exercise will be useful for future attempts to study Yangians in field and string theories, with or without supersymmetry 1 .

### Contents

, 2006

"... Let Λ be a preprojective algebra of Dynkin type, and let G be the corresponding complex semisimple simply connected algebraic group. We study rigid modules in subcategories SubQ for Q an injective Λ-module, and we introduce a mutation operation between complete rigid modules in SubQ. This yields clu ..."

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Let Λ be a preprojective algebra of Dynkin type, and let G be the corresponding complex semisimple simply connected algebraic group. We study rigid modules in subcategories SubQ for Q an injective Λ-module, and we introduce a mutation operation between complete rigid modules in SubQ. This yields cluster algebra structures on the coordinate rings of the partial

### Exact results for the low energy AdS4 × CP3 string theory

"... We derive the Thermodynamic Bethe Ansatz equations for the relativistic sigma model describing the AdS4 × CP3 string II A theory at strong coupling (i.e. in the Alday-Maldacena decoupling limit). The corresponding Y-system involves an infinite number of Y functions and is of a new type, although it ..."

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We derive the Thermodynamic Bethe Ansatz equations for the relativistic sigma model describing the AdS4 × CP3 string II A theory at strong coupling (i.e. in the Alday-Maldacena decoupling limit). The corresponding Y-system involves an infinite number of Y functions and is of a new type, although it shares a peculiar feature with the Y-system for AdS4 × CP3. A truncation of the equations at level p and a further generalisation to generic rank N allow us an alternative description of the theory as the N = 4, p = ∞ representative in an infinite family of models corresponding to the conformal cosets (CPN−1)p × U(1), perturbed by a relevant composite field φ(N,p) = φ[(CPN−1)p] × φ[U(1)] that couples the two independent conformal field theories. The calculation of the ultraviolet central charge confirms the conjecture by Basso and Rej and the conformal dimension of the perturbing operator, at every N and p, is obtained using the Y-system periodicity. The conformal dimension of φ[(CPN−1)p] matches that of the field identified by Fendley while discussing integrability issues for the purely bosonic CPN−1 sigma model.