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# Matrix Model for Structure Constants of Huge Protected Operators in N=4 SYM Theory

*by*

### Vladimir Kazakov

**Abstract:**

Huge operators in \( \mathcal{N} = 4\) SYM theory correspond to sources so heavy that they fully backreact on the space-time geometry. Here we study the protected correlation function of three such huge operators when they are given by \(1/2\) BPS operators , dual to IIB Strings in \(AdS_5 \times S^5\) . We unveil simple matrix model representations for these correlators which we can sometimes solve analytically. For general huge operators, we transform this matrix model into a \(1 + 1\) dimensional integrable hydrodynamics problem. A discrete counterpart of this system -â€“ the rational Calogero-Moser Model - helps to numerically solve the problem for general huge operators.

All talks Fall '24: New trends in QFT, modularity, resurgence