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Ref Arxiv: 1804.03399
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DOI: 10.1007/JHEP11(2018)204
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5 Citations
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We introduce and study conformal field theories specified by W −algebras commuting with certain set of screening charges. These CFT’s possess perturbations which define integrable QFT’s. We establish that these QFT’s have local and non-local Integrals of Motion and admit the perturbation theory in the weak coupling region. We construct factorized scattering theory which is consistent with non-local Integrals of Motion and perturbation theory. In the strong coupling limit the S−matrix of this QFT tends to the scattering matrix of the O(N) sigma model. The perturbation theory, Bethe ansatz technique, renormalization group approach and methods of conformal field theory are applied to show, that the constructed QFT’s are dual to integrable deformation of O(N) sigma-models.

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Ref Arxiv: 1802.07593
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DOI: 10.1088/1751-8121/aac976
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5 Citations
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We reconcile the Hamiltonian formalism and the zero curvature representation in the approach to integrable boundary conditions for a classical integrable system in 1  +  1 space-time dimensions. We start from an ultralocal Poisson algebra involving a Lax matrix and two (dynamical) boundary matrices. Sklyanin’s formula for the double-row transfer matrix is used to derive Hamilton’s equations of motion for both the Lax matrix and the boundary matrices in the form of zero curvature equations. A key ingredient of the method is a boundary version of the Semenov-Tian-Shansky formula for the generating function of the time-part of a Lax pair. The procedure is illustrated on the finite Toda chain for which we derive Lax pairs of size for previously known Hamiltonians of type BC N and D N corresponding to constant and dynamical boundary matrices respectively.

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Ref Arxiv: 1710.10665
DOI: 10.1007/JHEP01(2018)156
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8 Citations
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We study the rigid limit of a class of hypermultiplet moduli spaces appearing in Calabi-Yau compactifications of type IIB string theory, which is induced by a local limit of the Calabi-Yau. We show that the resulting hyperkahler manifold is obtained by performing a hyperkahler quotient of the Swann bundle over the moduli space, along the isometries arising in the limit. Physically, this manifold appears as the target space of the non-linear sigma model obtained by compactification of a five-dimensional gauge theory on a torus. This allows to compute dyonic and stringy instantons of the gauge theory from the known results on D-instantons in string theory. Besides, we formulate a simple condition on the existence of a non-trivial local limit in terms of intersection numbers of the Calabi-Yau, and find an explicit form for the hypermultiplet metric including corrections from all mutually non-local D-instantons, which can be of independent interest.

Commentaires: 38+18+5 pages, 2 figures

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Ref Arxiv: 1606.05495
DOI: 10.1007/s00029-018-0444-9
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7 Citations
Résumé:

Theta series for lattices with indefinite signature $(n_+,n_-)$ arise in many areas of mathematics including representation theory and enumerative algebraic geometry. Their modular properties are well understood in the Lorentzian case ($n_+=1$), but have remained obscure when $n_+\geq 2$. Using a higher-dimensional generalization of the usual (complementary) error function, discovered in an independent physics project, we construct the modular completion of a class of `conformal' holomorphic theta series ($n_+=2$). As an application, we determine the modular properties of a generalized Appell-Lerch sum attached to the lattice ${\operatorname A}_2$, which arose in the study of rank 3 vector bundles on $\mathbb{P}^2$. The extension of our method to $n_+>2$ is outlined.

Commentaires: 30 pages, 2 figures