New AdS$_2$ backgrounds and ${\cal N}=4$ Conformal Quantum Mechanics

TL;DR

The paper constructs an infinite family of Type IIB $AdS_2$ backgrounds preserving ${\cal N}=4$ SUSY by T-dualising seed AdS$_3$ massive IIA solutions, and proposes precise dual ${\cal N}=4$ superconformal quantum mechanics. It derives holographic observables, notably a central charge that counts SCQM vacua and matches the 2d seed central charge via DLCQ, and it uncovers non-perturbative Chern-Simons terms in the QM from D1/D5 probes. A RR-flux–driven extremisation principle is proposed, linking the central charge to an extremised functional of RR fluxes and to an electric–magnetic charge product, even in the presence of sources. Together, these results extend AdS$_2$/CFT$_1$ holography to richer ${\cal N}=4$ quantum mechanics with explicit boundary and flux data, offering concrete predictions for field-theory tests and future geometric extremisation studies.

Abstract

We present a new infinite family of Type IIB backgrounds with an AdS$_2$ factor, preserving ${\cal N}=4$ SUSY. For each member of the family we propose a precise dual Super Conformal Quantum Mechanics (SCQM). We provide holographic expressions for the number of vacua (the "central charge"), Chern-Simons terms and other non-perturbative aspects of the SCQM. We relate the "central charge" of the one-dimensional system with a combination of electric and magnetic fluxes in Type IIB. The Ramond-Ramond fluxes are used to propose an extremisation principle for the central charge. Other physical and geometrical aspects of these conformal quantum mechanics are analysed.

Figures (6)

• Figure 1: A generic quiver field theory whose IR is dual to the holographic background defined by the functions in \ref{['profileh4sp']}-\ref{['profileh8sp']}. The solid black lines represent $(4,4)$ hypermultiplets, the wavy lines represent $(0,4)$ hypermultiplets and the dashed lines represent $(0,2)$ Fermi multiplets. ${\cal N}=(4,4)$ vector multiplets are the degrees of freedom in each gauged node.
• Figure 2: On the left, we plot one cell in the Hanany-Witten set-up, in between the NS-five branes NS$_1$ and NS$_2$. The solid black lines represent $(4,4)$ hypermultiplets, the curvy lines $(0,4)$ hypermultiplets and the dashed lines $(0,2)$ Fermi multiplets. On the right, we plot the field content of one cell in the quiver (same convention). $Y,Z$ are $(4,4)$ hypers, $\Sigma$ denotes a $(0,4)$ hyper. The $(0,2)$ Fermi fields are denoted by $(\Psi,\widehat{\Psi})$. The gauge nodes contain $(4,4)$ vector multiplets.
• Figure 3: The Hanany-Witten set-up corresponding to the background in eqs.(\ref{['t dualised background NS']})-(\ref{['t dualised background RR']}).
• Figure 4: The quantum mechanical system that conjecturally flows in the IR to the SCQM described by the backgrounds obtained from eqs.(\ref{['profileh8exampleII']})-(\ref{['profileh4exampleII']}).
• Figure 5: Behaviour of the solutions at both ends of the $\rho$-interval for $u= u_0\rho$. The $\text{S}^2$ vanishes, while the $\text{S}^1_\psi$ is finite at $\rho=0$ but shrinks to zero size at $\rho=2\pi (P+1)$. The CY$_2$ has finite size at both ends.