Non-compact string backgrounds and non-rational CFT

Schomerus, Volker

doi:10.1016/j.physrep.2006.05.001

Cited by 45 publications

(78 citation statements)

References 127 publications

(179 reference statements)

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“…In particular, the significant progress of algebraic techniques in rational conformal field theory (RCFT) has been crucial to improve our knowledge on string compactification and string phenomenology. Nowadays the possibility of extending the systematic understanding gained in RCFT to non-RCFT in order to describe non-compact backgrounds is under active investigation (see [1] for a complete and comprehensive review).…”

Section: Introductionmentioning

confidence: 99%

“…Actually, a suitable number of these spectral flow operators has to be inserted in the correlation functions in order to transfer winding to the physical states. For instance the four-point function of three generic states and one spectral flow operator was computed in [4] in order to obtain the one unit spectral flow three-point function 1 . The same method was used in [6,7] to compute the five-point function involving three generic states and two spectral flow operators, leading to the spectral flow conserving three-point function of two w = 1 and one w = 0 states 2 .…”

Section: Introductionmentioning

confidence: 99%

“…The problem of constructing a complete set of solutions to the KZ equations for generic four-point functions has not been solved yet. These equations cannot be reduced to a system of ordinary differential equations [8] as in the case of the compact SU (2) WZNW model [9] and thus the bootstrap approach does 1 A well known feature of string interactions is that winding number conservation may be violated according to a precise pattern determined by the properties of SL(2, R) representations [4,6]. 2 Recall that w takes positive integer values in the x−basis [4].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Coulomb integrals for theSL(2,R)Wess-Zumino-Novikov-Witten model

Iguri

Núñez

2008

Phys. Rev. D

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We review the Coulomb gas computation of three-point functions in the SL(2, R) WZNW model and obtain explicit expressions for generic states. These amplitudes have been computed in the past by this and other methods but the analytic continuation in the number of screening charges required by the Coulomb gas formalism had only been performed in particular cases. After showing that ghost contributions to the correlators can be generally expressed in terms of Schur polynomials, we solve Aomoto integrals in the complex plane, a new set of multiple integrals of Dotsenko-Fateev type. We then make use of monodromy invariance to analytically continue the number of screening operators and prove that this procedure gives results in complete agreement with the amplitudes obtained from the bootstrap approach. We also compute a four-point function involving a spectral flow operator and we verify that it leads to the one unit spectral flow three-point function according to a prescription previously proposed in the literature. In addition, we present an alternative method to obtain spectral flow non-conserving n−point functions through well defined operators and we prove that it reproduces the exact correlators for n = 3. Independence of the result on the insertion points of these operators suggests that it is possible to violate winding number conservation modifying the background charge. *

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Coulomb integrals for theSL(2,R)Wess-Zumino-Novikov-Witten model

Iguri

Núñez

2008

Phys. Rev. D

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“…Most importantly, we shall discuss the spectrum of primary fields along with their 2-and 3-point functions. For a more details see the reviews [15,16,17].…”

Section: Review Of Liouville Field Theorymentioning

confidence: 99%

“…the reviews [20,15,16] for references). Full crossing symmetry of the conjectured 3-point function was established much later in two steps by Ponsot and Teschner [21] and by Teschner [15,22].…”

Section: Bosonic Liouville Field Theorymentioning

confidence: 99%

Liouville’s imaginary shadow

Schomerus¹,

Suchanek

2012

J. High Energ. Phys.

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N=1 super Liouville field theory is one of the simplest non-rational conformal field theories. It possesses various important extensions and interesting applications, e.g. to the AGT relation with 4D gauge theory or the construction of the OSP(1|2) WZW model. In both setups, the N=1 Liouville field is accompanied by an additional free fermion. Recently, Belavin et al. suggested a bosonization of the product theory in terms of two bosonic Liouville fields. While one of these Liouville fields is standard, the second turns out to be imaginary (or time-like). We extend the proposal to the R sector and perform extensive checks based on detailed comparison of 3-point functions involving several super-conformal primaries and descendants. On the basis of such strong evidence we sketch a number of interesting potential applications of this intriguing bozonization.

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Lattice regularisation of a non-compact boundary conformal field theory

Robertson

Jacobsen

Saleur

2021

J. High Energ. Phys.

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Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such CFTs have been identified as the continuum limits of lattice models with a finite number of degrees of freedom per site. However, results have so far been restricted to the case of periodic boundary conditions, precluding the exploration via lattice models of aspects of non-compact boundary CFTs and the corresponding D-brane constructions.The present paper follows a series of previous works on a ℤ2-staggered XXZ spin chain, whose continuum limit is known to be a non-compact CFT related with the Euclidian black hole sigma model. By using the relationship of this spin chain with an integrable $$ {D}_2^2 $$ D 2 2 vertex model, we here identify integrable boundary conditions that lead to a continuous spectrum of boundary exponents, and thus correspond to non-compact branes. In the context of the Potts model on a square lattice, they correspond to wired boundary conditions at the physical antiferromagnetic critical point. The relations with the boundary parafermion theories are discussed as well. We are also able to identify a boundary renormalisation group flow from the non-compact boundary conditions to the previously studied compact ones.

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Non-compact string backgrounds and non-rational CFT

Cited by 45 publications

References 127 publications

Coulomb integrals for theSL(2,R)Wess-Zumino-Novikov-Witten model

Coulomb integrals for theSL(2,R)Wess-Zumino-Novikov-Witten model

Liouville’s imaginary shadow

Lattice regularisation of a non-compact boundary conformal field theory

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