Calogero-Sutherland approach to defect blocks

Isachenkov, Mikhail; Liendo, Pedro; Linke, Yannick; Schomerus, Volker

doi:10.1007/jhep10(2018)204

Cited by 57 publications

(97 citation statements)

References 76 publications

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“…The connection uncovered in [17] implies that conformal blocks are certain multivariable hypergeometric functions with properties that follow from integrability of the quantum mechanical system and are very similar to those of ordinary hypergeometrics in one variable. Later, it was shown that the relation between conformal blocks and Calogero-Sutherland models is universal in that it applies to spinning and defect blocks etc, see [19][20][21].…”

Section: Contentsmentioning

confidence: 99%

“…Such a configuration admits two channels, the defect and the bulk channel [21,[61][62][63]. While defect channel blocks split into simple products of hypergeometric functions in one variable [61], the construction for bulk channel blocks with scalar external fields was only completed recently in [21], see also [62] for earlier results. An extension to bulk channel blocks for spinning operators was initiated recently in [63].…”

Section: Applications To 4-dimensional N = 1 Theoriesmentioning

confidence: 99%

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Superconformal blocks: general theory

Burić

Schomerus

Sobko

2020

J. High Energ. Phys.

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In this work we launch a systematic theory of superconformal blocks for four-point functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number N of supersymmetries. The central new ingredient is a universal construction of the relevant Casimir differential equations. In order to find these equations, we model superconformal blocks as functions on the supergroup and pick a distinguished set of coordinates. The latter are chosen so that the superconformal Casimir operator can be written as a perturbation of the Casimir operator for spinning bosonic blocks by a fermionic (nilpotent) term. Solutions to the associated eigenvalue problem can be obtained through a quantum mechanical perturbation theory that truncates at some finite order so that all results are exact. We illustrate the general theory at the example of d = 1 dimensional theories with N = 2 supersymmetry for which we recover known superblocks. The paper concludes with an outlook to 4-dimensional blocks with N = 1 supersymmetry.

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Section: Contentsmentioning

confidence: 99%

Section: Applications To 4-dimensional N = 1 Theoriesmentioning

confidence: 99%

Superconformal blocks: general theory

Burić

Schomerus

Sobko

2020

J. High Energ. Phys.

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“…New connections to mathematics and new applications are still coming to light in the current literature, see e.g. [6,7,22,24,46,53].The richness of these models is also due to their many generalizations and deformations. These are associated with different interaction potentials (from rational to elliptic), root systems and extensions with internal degrees of freedom.…”

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confidence: 99%

“…New connections to mathematics and new applications are still coming to light in the current literature, see e.g. [6,7,22,24,46,53].…”

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confidence: 99%

Poisson-Lie analogues of spin Sutherland models

Fehér

2019

Nuclear Physics B

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We present generalizations of the well-known trigonometric spin Sutherland models, which were derived by Hamiltonian reduction of 'free motion' on cotangent bundles of compact simple Lie groups based on the conjugation action. Our models result by reducing the corresponding Heisenberg doubles with the aid of a Poisson-Lie analogue of the conjugation action. We describe the reduced symplectic structure and show that the 'reduced main Hamiltonians' reproduce the spin Sutherland model by keeping only Integrable systems of particles moving in one dimension have been studied intensively for nearly 50 years, beginning with the pioneering papers of Calogero [5], Sutherland [51] and Moser [35]. Thanks to their fascinating mathematics and diverse applications [10,37,38,44,52], the interest in these models shows no sign of diminishing. New connections to mathematics and new applications are still coming to light in the current literature, see e.g. [6,7,22,24,46,53].The richness of these models is also due to their many generalizations and deformations. These are associated with different interaction potentials (from rational to elliptic), root systems and extensions with internal degrees of freedom. We call 'Sutherland models' the systems defined by trigonometric or hyperbolic potentials. For all these systems, classical and quantum mechanical versions are studied separately, and one needs to pay attention to the distinct features of the systems with real particle positions and their complexifications. The investigations of Ruijsenaars-Schneider (RS) type deformations [44,45] is motivated, for example, by relations to solitons, spin chains, special functions and double affine Hecke algebras.The internal degrees of freedom are colloquially called 'spin', and can be of two rather different kinds. First, the point particles can carry spins varying in a vector space, as is the case for the Gibbons-Hermsen models [20] and their RS type generalizations introduced by Krichever and Zabrodin [28]. Second, the models can involve a collective spin variable that typically belongs to a coadjoint orbit, and is not assigned separately to the particles. An example of this second type is the trigonometric spin Sutherland model defined classically by a Hamiltonian of the following form:

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“…More recently, Lorentzian CFT's have attracted renewed interest in light of the novel development in analytic bootstrap in lightcone [20][21][22], the Regge limits of correlation functions [23][24][25][26][27], and the remarkable applications in deriving averaged null energy condition in flat space [28,29] and the Lorentzian inversion formula [30,31]. Conformal blocks play a vital role also there as a probe of causal relationships between operators in Minkowski space, whose structures have been deeply tied to a class of quantum integrable systems in the past few years [32][33][34].…”

Section: Contentsmentioning

confidence: 99%

The gravity dual of Lorentzian OPE blocks

Chen

Kobayashi

et al. 2020

J. High Energ. Phys.

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We consider the operator product expansion (OPE) structure of scalar primary operators in a generic Lorentzian CFT and its dual description in a gravitational theory with one extra dimension. The OPE can be decomposed into certain bi-local operators transforming as the irreducible representations under conformal group, called the OPE blocks. We show the OPE block is given by integrating a higher spin field along a geodesic in the Lorentzian AdS space-time when the two operators are space-like separated. When the two operators are time-like separated however, we find the OPE block has a peculiar representation where the dual gravitational theory is not defined on the AdS space-time but on a hyperboloid with an additional time coordinate and Minkowski space-time on its boundary. This differs from the surface Witten diagram proposal for the time-like OPE block, but in two dimensions we reproduce it consistently using a kinematical duality between a pair of time-like separated points and space-like ones.

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Calogero-Sutherland approach to defect blocks

Cited by 57 publications

References 76 publications

Superconformal blocks: general theory

Superconformal blocks: general theory

Poisson-Lie analogues of spin Sutherland models

The gravity dual of Lorentzian OPE blocks

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