A generalized dominance ordering for 1/2-BPS states

Abstract

Abstract We discuss a generalized dominance ordering for irreducible representations of the symmetric group S n with the aim of distinguishing the corresponding states in the 1/2-BPS sector of U(N) Super Yang-Mills theory when a certain finite number of Casimir operators are known. Having knowledge of a restricted set of Casimir operators was proposed as a mechanism for information loss in this sector and its dual gravity theory in AdS5 × S 5. It is well-known that the states in this sector are labeled by Young diagrams with n boxes. We propose a generalization of the well-known dominance ordering of Young diagrams. Using this generalization, we posit a conjecture to determine an upper bound for the number of Casimir operators needed to distinguish between the 1/2-BPS states and thus also between their duals in the gravity theory. We offer numerical and analytic evidence for the conjecture. Lastly, we discuss implications of this conjecture when the energy n of the states is asymptotically large.

Keywords

• AdS-CFT Correspondence
• Black Holes in String Theory
• Gauge-Gravity Correspondence