Enhanced symmetries of gauge theory and resolving the spectrum of local operators

Abstract

Enhanced global non-abelian symmetries at zero coupling in Yang Mills theory play an important role in diagonalising the two-point functions of multi-matrix operators. Generalised Casimirs constructed from the iterated commutator action of these enhanced symmetries resolve all the multiplicity labels of the bases of matrix operators which diagonalise the two-point function. For the case of U (N) gauge theory with a single complex matrix in the adjoint of the gauge group we have a U(N)^{\times 4} global symmetry of the scaling operator at zero coupling. Different choices of commuting sets of Casimirs, for the case of a complex matrix, lead to the restricted Schur basis previously studied in connection with string excitations of giant gravitons and the Brauer basis studied in connection with brane-anti-brane systems. More generally these remarks can be extended to the diagonalisation for any global symmetry group G. Schur-Weyl duality plays a central role in connecting the enhanced symmetries and the diagonal bases.

45 pages, no figures. Revised version : added refs, corrected typos

References in corpus (8)

• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Giant Gravitons - with Strings Attached (III)
• Giant Gravitons - with Strings Attached (II)
• Integrability vs. Information Loss: A Simple Example
• Schur-Weyl duality as an instrument of Gauge-String duality
• Permutations and the Loop
• A New Approach to the Representation Thoery of the Symmetric Groups. 2

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