N=4 Superconformal Mechanics and Black Holes

TL;DR

This paper develops an extended N=4 superconformal mechanics model coupled with multiple vector supermultiplets, revealing how black hole charges emerge from auxiliary component constraints and providing explicit actions and Hamiltonians.

Contribution

It introduces a novel N=4 superconformal mechanics framework with special Kahler geometry, explicitly demonstrating the emergence of black hole charges from auxiliary fields.

Findings

Constructed an N=4 superconformal mechanics model with vector multiplets.

Derived explicit component action, supercharges, and Hamiltonian.

Presented a modified black hole potential with non-zero auxiliary components.

Abstract

The motion of a particle near the Reissner-Nordstrom black hole horizon is described by conformal mechanics. In this paper we present an extended one-dimensional analysis of the N=4 superconformal mechanics coupled to n copies of N=8, d=1 vector supermultiplets. The constructed system possesses a special Kahler geometry in the scalar sector of the vector multiplets as well as an N=4 superconformal symmetry which is provided by a proper coupling to a dilaton superfield. The superconformal symmetry completely fixes the resulting action. We explicitly demonstrate that the electric and magnetic charges, presenting in the "effective black hole" action, appear as a result of resolving constraints on the auxiliary components of the vector supermultiplets. We present the component action, supercharges and Hamiltonian with all fermionic terms included. One of the possible ways to generalize the black hole potential is to consider a modified version of the N=4 superconformal multiplet where its auxiliary components acquire non-zero constant values. We explicitly write down the corresponding modified black hole potential.