Integrable Wilson loops
By N. Drukker. 2012
181 citations recorded by the source corpus.
A bstractThe generalized quark-antiquark potential of $ \mathcal{N}=4 $ supersymmetric Yang-Mills theory on $ {{\mathbb{S}}^3}\times \mathbb{R} $ calculates the potential between a pair of heavy charged particles separated by an arbitrary angle on $ {{\mathbb{S}}^3} $ and also an angle in flavor space. It can be calculated by a Wilson loop following a prescribed path and couplings, or after a conformal transformation, by a cusped Wilson loop in flat space, hence also generalizing the usual concept of the cusp anomalous dimension. In $ \mathbb{A}\mathrm{d}{{\mathrm{S}}_5}\times {{\mathbb{S}}^5} $ this is calculated by an infinite open string. I present here an open spin-chain model which calculates the spectrum of excitations of such open strings. In the dual gauge theory these are cusped Wilson loops with extra operator insertions at the cusp. The boundaries of the spin-chain introduce a non-trivial reflection phase and break the bulk symmetry down to a single copy of $ \mathfrak{p}\mathfrak{s}\mathfrak{u}\left( {\left. 2 \right|2} \right) $. The dependence on the two angles is captured by the two embeddings of this algebra into $ \mathfrak{p}\mathfrak{s}\mathfrak{u}{{\left( {\left. 2 \right|2} \right)}^2} $, i.e., by a global rotation. The exact answer to this problem is conjectured to be given by solutions to a set of twisted boundary thermodynamic Bethe ansatz integral equations. In particular the generalized quark-antiquark potential or cusp anomalous dimension is recovered by calculating the ground state energy of the minimal length spin-chain, with no sites. It gets contributions only from virtual particles reflecting off the boundaries. I reproduce from this calculation some known weak coupling perturtbative results.
Subfields: Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/e0a341a800f063026ab44f2991e146d73a7dd210
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Citations in the corpus
- Hexagonalization of correlation functions (2016, background): “Since the (15)See for instance [21, 22], where the same character appears in a different context.”
- Half-BPS Wilson loop and AdS2/CFT1 (2017, result): “In principle, the spectrum of dimensions of operators inserted on the Wilson line should be accessible from the TBA approach of [35,36], and it would be interesting to reproduce our results in this integrability-based framework.”
- Quantum spectral curve for arbitrary state/operator in AdS5/CFT4 (2014, methodology): “Further development of our methods should also allow for a comprehensive description of the open strings spectrum with various types of integrable boundary conditions, which cover such physically relevant cases as quark–anti-quark potential [25, 26], DD̄-systems [27].”
- Exact results for the entanglement entropy and the energy radiated by a quark (2013, methodology): “If it were possible to also derive an expression for this function using integrability (as it was done for N = 4 super Yang Mills in [18, 19]), then by comparing the two answers one could compute a non-trivial function of the t’Hooft coupling that appears in all the ABJM results obtained via integra”