Generalised twisted partition functions

By V. Petkova, Jean-Bernard Zuber. 2000

346 citations recorded by the source corpus.

Abstract We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D conformal field theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a92db275adc6ade1043da7f451c6b0843268307e

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Citations in the corpus

Topological defect lines and renormalization group flows in two dimensions (2018, methodology): “We then move on to considering TDLs in more general RCFTs, and further discuss their relations to orbifolds and dualities.”
The many faces of Ocneanu cells (2001, methodology): “a: ˜nx˜ny= X z Ne xy zn˜ z , (1.3) Ne x Ne y= X z Ne xy zNe z. (1.4) This algebra admits an interpretation as the algebra of the twist operators used in the construction of the partition functions in [8]. It is associated with the Ocneanu graph Ge in the sense of the relation V˜ ij Ne x= X z V˜ ij;x”
TFT construction of RCFT correlators I: Partition functions (2002, background): “10 Defect lines and double fusion algebra In this section we consider the partition function of a torus with two defect lines inserted – a setup studied in [34].”
TFT construction of RCFT correlators: III: simple currents (2004, background): “This is the way the fusion algebra of defect lines was introduced in [72].”
The virtue of defects in 4D gauge theories and 2D CFTs (2010, background): “Topological loop operators [6] are labeled by a (homotopy class of a) curve on the Riemann surface where the CFT is defined and by a representation of the chiral algebra A of the CFT (the Virasoro algebra for Liouville theory and a W -algebra for Toda CFTs).”
TFT construction of RCFT correlators IV: Structure constants and correlation functions (2004, background): “rules [40]; as follows from the ribbon representation (I:5.”
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond (2022, background): “27 In rational CFT [81, 84, 85], there is a general construction of topological lines that commute with the extended chiral algebra [86,87].”
TFT construction of RCFT correlators II: unoriented world sheets (2003, background): “Rational conformal defects with the same CFT on either side have been studied in [68–70,73].”
DEFECT LINES, DUALITIES AND GENERALISED ORBIFOLDS (2009, methodology): “Topological defects preserve more symmetry, and for these the situation is better: one knows all topological defects for the Virasoro minimal models [9] and for the free boson [10].”