Abstract
We explain how the ’t Hooft expansion of correlators of half-BPS operators can be resummed in a large-charge limit in mathcal{N} = 4 super Yang-Mills theory. The full correlator in the limit is given by a non-trivial function of two variables: One variable is the charge of the BPS operators divided by the square root of the number Nc of colors; the other variable is the octagon that contains all the ’t Hooft coupling and spacetime dependence. At each genus g in the large Nc expansion, this function is a polynomial of degree 2g + 2 in the octagon. We find several dual matrix model representations of the correlators in the large-charge limit. Amusingly, the number of colors in these matrix models is formally taken to zero in the relevant limit.
Highlights
Determined exactly in [1, 2] at any value of the ’t Hooft coupling and further simplified into an infinite determinant representation in [3]
The full correlator in the limit is given by a non-trivial function of two variables: One variable is the charge of the BPS operators divided by the square root of the number Nc of colors; the other variable is the octagon that contains all the ’t Hooft coupling and spacetime dependence
The main result of this paper is a representation of the function A and of the associated polynomials Pg+1 in (1.4) in terms of a matrix model, where the octagon function O enters as an effective quartic coupling
Summary
The basis of our computation is the (planar and non-planar) hexagonalization prescription for correlation functions [10,11,12,13,14,15]. To obtain the full correlator (2.9) at genus g from the matrix model (2.4), we bring down 2g + 2 vertices, pick the N 4 coefficient As usual with such graph dualities, N is not to be identified with the Nc of N = 4 SYM, see e.g. N 4 would be replaced by N1N2N3N4, identifying precisely the four faces corresponding to the four distinct operators The terms containing this factor automatically contain all ki, so using rectangular matrices would allow us to condense the instructions above into . Be fascinating to slowly decrease the size of our BPS operators to move away from our fully convergent limit and carefully isolate these novel effects in a controllable way
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