Multi-graded Galilean conformal algebras

Ragoucy, É.; Rasmussen, Jørgen; Raymond, Christopher

doi:10.1016/j.nuclphysb.2020.115092

Cited by 5 publications

(9 citation statements)

References 89 publications

(150 reference statements)

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“…Here we provide a specific examples of the operators that arise. We consider the multi-graded affine Lie algebra g 2,3 G , that is, we have N = 6. The set of sequences 0 i ≺ 2, 3 is given in canonical order by I 2,3 = {0, 0; 0, 1; 0, 2; 1, 0; 1, 1; 1, 2}.…”

Section: Gal Galmentioning

confidence: 99%

“…The following Chapter is based on work currently in preparation to appear as [3] E. Ragoucy, J. Rasmussen, C. Raymond, Asymmetric Galilean contractions.…”

Section: Gal Galmentioning

confidence: 99%

“…In Section 6.2, we looked at the specific example of the module [0] P λ 1,0 ;1,0 ∈ M (2,3). In this section we will consider the staggered modules which have the same component module conformal weights, however, we allow the value of the central charge to be any admissible value.…”

Section: Symmetries Of Staggered Modules In M(2 3)mentioning

confidence: 99%

“…(and equivalently [i] P p+t,u−1,v−1 ) in all possible minimal models, in particular, we have also determined the structure for the corresponding family in M (3,2). In order to better understand this module, as well as provide explicit examples for some of our previous results, we will continue by looking at the spectral flows of this module.…”

Section: Symmetries Of Staggered Modules In M(2 3)mentioning

confidence: 99%

“…Correspondingly, the N = 2 superconformal algebras are vertex operator superalgebras, generated by two bosonic fields, namely J(z), T (z) of conformal weight 1 and 2 respectively, and two fermionic fields G ± (z) each of conformal weight 3 2 . The field T (z) generates a Virasoro subalgebra, and the other generating fields are primary.…”

Section: Introduction To the N = 2 Superconformal Algebrasmentioning

confidence: 99%

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Algebraic aspects of conformal field theory

Raymond¹

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This thesis presents an algebraic study of two areas of conformal field theory. The first part extends the theory of Galilean conformal algebras. These algebras are extended conformal symmetry algebras for two-dimensional quantum field theories, formed through a process known as Galilean contraction. Analogous to an Inonu-Wigner contraction, the Galilean contraction procedure takes two conformal symmetry algebras, equivalent up to central charge, as input and produces a new conformal symmetry algebra. We extend the theory of Galilean contractions in several directions. First, we develop the theory to allow input of any number of symmetry algebras. These generalised algebras have a truncated graded structure. We develop a theory for multi-graded Galilean algebras, whereby we can extend structures which are graded by sequences. Finally, we present a comprehensive analysis of the possible algebras which arise when the input algebras are no longer required to be equivalent. We refer to this as the asymmetric Galilean contraction. For each stage of generalisation, we present several pertinent examples, discuss the Sugawara construction of a Galilean Virasoro algebra given an affine Lie algebra, and apply our results to the W-algebra W 3. The second part of this thesis presents an exploratory study of reducible but indecomposable modules of the N = 2 Superconformal algebras, known as staggered modules. These modules are characterised by a non-diagonalisable action of L 0 , the Virasoro zero-mode. Using recent results on the coset construction of N = 2 minimal models, we are able to construct the first examples of staggered modules for the N = 2 algebras. We determine the structure of a family of such modules for all admissible values of the central charge. Furthermore, we investigate the action of symmetries such as spectral flow on these modules. We present the results along with a range of examples, and discuss possible paths towards a classification of such modules for the Neveu-Schwarz and Ramond N = 2 superconformal algebras.

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Section: Gal Galmentioning

confidence: 99%

“…The following Chapter is based on work currently in preparation to appear as [3] E. Ragoucy, J. Rasmussen, C. Raymond, Asymmetric Galilean contractions.…”

Section: Gal Galmentioning

confidence: 99%

Section: Symmetries Of Staggered Modules In M(2 3)mentioning

confidence: 99%

Section: Symmetries Of Staggered Modules In M(2 3)mentioning

confidence: 99%

Section: Introduction To the N = 2 Superconformal Algebrasmentioning

confidence: 99%

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Algebraic aspects of conformal field theory

Raymond¹

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Non-Lorentzian Kač-Moody algebras

Bagchi

Ritankar

Kaushik

et al. 2023

J. High Energ. Phys.

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We investigate two dimensional (2d) quantum field theories which exhibit Non-Lorentzian Kač-Moody (NLKM) algebras as their underlying symmetry. Our investigations encompass both 2d Galilean (speed of light c → ∞) and Carrollian (c → 0) CFTs with additional number of infinite non-Abelian currents, stemming from an isomorphism between the two algebras. We alternate between an intrinsic and a limiting analysis. Our NLKM algebra is constructed first through a contraction and then derived from an intrinsically Carrollian perspective. We then go on to use the symmetries to derive a Non-Lorentzian (NL) Sugawara construction and ultimately write down the NL equivalent of the Knizhnik Zamolodchikov equations. All of these are also derived from contractions, thus providing a robust cross-check of our analyses.

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