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arXiv:2411.01774

Four-twist effects and monodromy in symmetric orbifold CFTs

Bin Guo, Shaun D. Hampton

Published Nov 4, 2024• 0 citations
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Abstract

Symmetric orbifold CFTs contain twist operators that can join and split copies of the CFT, leading to the creation of pairs from the vacuum. In this paper, we study the pair creation processes involving four twist-2 operators. In addition to the pair creation previously observed purely in the left or right moving sectors, we find a novel mixing between left and right movers during pair creation. This phenomenon arises from nontrivial monodromy conditions that originate from a genus-one covering surface, where left and right movers become coupled through the torus.

DOI
10.48550/arxiv.2411.01774

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Symmetric orbifold CFTs contain twist operators that can join and split copies of the CFT, leading to the creation of pairs from the vacuum. In this paper, we study the pair creation processes involving four twist-2 operators. In addition to the pair creation previously observed purely in the left or right moving sectors, we find a novel mixing between left and right movers during pair creation. This phenomenon arises from nontrivial monodromy conditions that originate from a genus-one covering surface, where left and right movers become coupled through the torus.
Symmetric orbifold CFTs contain twist operators that can join and split copies of the CFT. In this paper, we study the effects of four twist-2 operators on two copies of a single free boson. A recent study analyzed their effects on the vacuum, finding a nontrivial left-right mixing that arises from the fact that the covering surface is a torus, while the effects of one or two twist-2 operators do not produce such mixing. Here, we extend this analysis to excited states and find a similar left-right mixing. Furthermore, we explore the continuum, or high-energy, limit and show that the left-right mixing becomes negligible in this limit.
A bstract Orbifold CFTs contain twist operators that can join and split copies of the CFT. In this paper, we study the effects of four twist-2 operators on two copies of a single free boson. A recent study analyzed their effects on the vacuum, finding a nontrivial left-right mixing that arises from the fact that the covering surface is a torus, while the effects of one or two twist-2 operators do not produce such mixing. Here, we extend this analysis to excited states and find a similar left-right mixing. Furthermore, we explore the continuum, or high-energy, limit and show that the left-right mixing becomes negligible in this limit.
Abstract We study the 2D symmetric orbifold CFT of two copies of free bosons. The twist operator can join the two separated copies in the untwisted sector into a joined copy in the twisted sector. Starting with a state with any number of quanta in the untwisted sector, the state in the twisted sector obtained by the action of the twist operator can be computed by using the covering map method. We develop a new method to compute the effect of a twist operator by using the Bogoliubov ansatz and conformal symmetry. This may lead to more efficient tools to compute correlation functions involving twist operators.
Abstract In this work, we explore the twist operator OPEs of a generic bosonic symmetric product (S N ) orbifold CFT. We conjecture that at large N the OPE of bare twist operators contains only bare twists and excitations of bare twists with fractional Virasoro modes. These fractionally excited operators are the only ones that depend exclusively on the lengths of the twists and the central charge, agreeing with the general structure of correlators of bare twists at large N found in the literature. To provide evidence for this, we study the coincidence limit of a four point function of bare twist operators to several non-leading orders. We show how the coefficients of these powers can be reproduced by considering bare twist operators excited by fractional Virasoro modes in the exchange channels.
We show that 1+11+11+1 dimensional vacua of the (0,2)(0,2)(0,2) heterotic string have many properties in common with more recently studied physical systems. The free theory exhibits a symmetric product CFT structure. The single-string Hilbert space splits into sectors labeled by the string winding, www, that contain purely left-moving (for w>0w>0w>0) and right-moving (for w<0w<0w<0) excitations. These sectors exhibit infinite-dimensional left and right-moving symmetry algebras, respectively, with central extensions that depend on www. String interactions between left and right-movers appear to lead to a TTˉT\bar TTTˉ deformation of the free theory.
We exploit null vectors of the fractional Virasoro algebra of the symmetric product orbifold to compute correlation functions of twist fields in the large N limit. This yields a new method to derive correlation functions in these orbifold CFTs that is purely based on the symmetry algebra. We explore various generalisations, such as subleading (torus) contributions or correlation functions of other fields than the bare twist fields. We comment on the consequences of our computation for the AdS3/CFT2 correspondence.