Browsing by Author "Carlson, Warren Anthony"

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    The geometry and topology of the gauge theory/gravity correspondence
    (2011-03-09) Carlson, Warren Anthony
    The well studied AdS/CFT correspondence describes a duality between gauge theories and string theories. What is currently lacking is a dictionary translating gauge theory correlators in space-time to string theory correlators on a world-sheet. We investigate aspects of world-sheet correlators of closed string theories dual to large N SU(N) gauge theories following a prescription by Gopakumar. The prescription presents a concrete mapping of gauge theory correlators to string theory correlators. Gauge theory correlators are translated to string world-sheet correlators via a reparametrization by inverse Schwinger parameters and a mapping to the moduli space of Riemann surfaces (worldsheets) via a special class of quadratic differentials know as Strebel differentials.
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    The Large N Limit of Heavy Operator Excitations
    (University of the Witwatersrand, Johannesburg, 2023-07) Carlson, Warren Anthony; De Mello Koch, Robert
    Operators with bare dimension of order N are studied. These are restricted Schur polynomials labeled by Young diagrams with two long rows or two long columns and are heavy operators in the large N limit. A dramatic simplification of the action of the dilatation operator on these states is found, where the diagonalization of the dilatation operator reduces to solving three-term recursion relations. The solutions to these recursion relations reduce the spectrum of the dilatation operator to that of decoupled harmonic oscillators, showing that these systems are integrable at large N. Then, generating functions for bound states of two giant gravitons are constructed and an extension to more than two giant gravitons is sketched. These generating functions are integrals over auxiliary variables that encode the symmetrization and anti-symmetrization of the fields in the restricted Schur polynomials and give a simple construction of eigenfunctions of the dilatation operator. These generating functions are shown to be eigenfunctions of the dilatation operator in the large N limit. As a byproduct, this construction gives a natural starting point for systematic 1/N expansions of these operators. This includes the prospect to generate asymptotic representations of the symmetric group and its characters via the restricted Schur polynomials. Finally, the asymptotic expansion of the three-point function is computed in three BMN limits by varying one parameter in the large N limit. It is argued that these asymptotic expansions encode non-perturbative effects and are related by a parametric Stokes phenomenon.