The Chiral Random-Matrix Ensemble of the Type-IIB Axion--Dilaton Wormhole Partition Function

Abstract

I construct a microscopic ADHM/chiral-Wishart representative of the reduced charge-sector coefficient $W_ν[b]$ that enters the Type-IIB axion--dilaton wormhole partition function $Z_{\rm wh}(θ;b)$. I fix the axion-charge sector, equivalently the form-field-flux sector, which plays the exact same structural role as a fixed-topology sector in QCD: it supplies the domain where I compute the microscopic coefficient before forming the final theta sum. At $E=0$, the axion--dilaton radial family reaches its BPS instanton endpoint. After I impose the Hamiltonian constraint, gauge quotient, charge-sector boundary condition, and collective zero-mode quotient, the physical quadratic fluctuation operator at that endpoint becomes a positive adjoint square. Its non-zero spectrum is therefore a squared singular-value spectrum, and its microscopic endpoint is a Laguerre/chiral hard edge. The D(-1)/D3 super-ADHM collective-coordinate integral supplies the Type-IIB microscopic representative of this same coefficient. In the large$N$ result of Dorey et al., this super-ADHM measure becomes the $k$-D-instanton measure on $AdS_5\times S^5$, multiplied by a centered zero-dimensional supersymmetric matrix-model factor. The chiral/Wishart ensemble forms the hard-edge limit of the rectangular block inside this super-ADHM integral. Fermionic ADHM variables and supergravity fermions remain part of the coefficient: in protected sectors they cancel paired non-zero modes, impose zero-mode saturation, and determine which reduction data \(b\) give a non-vanishing $W_ν[b]$.