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AdS_3 x S^3 x S^3 x S^1 Solutions of Type IIB String Theory

Aristomenis Donos, Jerome P. Gauntlett, James Sparks

TL;DR

The paper constructs globally well-defined AdS$_3$ backgrounds in Type IIB supergravity whose internal space is $S^3 imes S^3 imes S^1$, starting from local AdS$_3$ solutions with NS flux and dilaton. A step-by-step topological assembly—$B_4 o S^2 imes S^2$, then $M_5 o S^3 imes S^2$, then $M_6 o S^3 imes S^3$—is augmented by a quotient to enable integral three-form flux; flux quanta $(M_1,M_2)$ are tied to coprime integers $(p,q)$ via $M_1=M(p+q)^2$ and $M_2=Mq^2$, and the central charge is $c=6n_1 rac{(M_1-M_2)M_2}{M_1}$, independent of the deformation parameter $Q$. The authors show that $Q eq0$ deformations yield a continuous family with the same $c$, interpreted as exactly marginal in the dual $(0,2)$ SCFT, while limits as $Q o0$ reveal subtleties in global identifications. They further extend the construction to more general identifications, maintaining the same central-charge structure but with more flexible flux data. Overall, the work provides a concrete global realization of a rich AdS$_3$ class in IIB, clarifying flux quantisation, topology, and holographic data for a family of $(0,2)$ SCFTs. Key results include the explicit global topology $S^3 imes S^3 imes S^1$, the flux-quantisation prescription via the $Z_{(p+q)q}$ quotient, and the central charge formula that connects geometric data to CFT characteristics. This advances the understanding of AdS$_3$/CFT$_2$ in string theory by producing new globally well-defined backgrounds with nontrivial fluxes and outlining a pathway to their holographic interpretation.

Abstract

We analyse a recently constructed class of local solutions of type IIB supergravity that consist of a warped product of AdS_3 with a seven-dimensional internal space. In one duality frame the only other non-vanishing fields are the NS three-form and the dilaton. We analyse in detail how these local solutions can be extended to globally well-defined solutions of type IIB string theory, with the internal space having topology S^3 x S^3 x S^1 and with properly quantised three-form flux.

AdS_3 x S^3 x S^3 x S^1 Solutions of Type IIB String Theory

TL;DR

The paper constructs globally well-defined AdS backgrounds in Type IIB supergravity whose internal space is , starting from local AdS solutions with NS flux and dilaton. A step-by-step topological assembly—, then , then —is augmented by a quotient to enable integral three-form flux; flux quanta are tied to coprime integers via and , and the central charge is , independent of the deformation parameter . The authors show that deformations yield a continuous family with the same , interpreted as exactly marginal in the dual SCFT, while limits as reveal subtleties in global identifications. They further extend the construction to more general identifications, maintaining the same central-charge structure but with more flexible flux data. Overall, the work provides a concrete global realization of a rich AdS class in IIB, clarifying flux quantisation, topology, and holographic data for a family of SCFTs. Key results include the explicit global topology , the flux-quantisation prescription via the quotient, and the central charge formula that connects geometric data to CFT characteristics. This advances the understanding of AdS/CFT in string theory by producing new globally well-defined backgrounds with nontrivial fluxes and outlining a pathway to their holographic interpretation.

Abstract

We analyse a recently constructed class of local solutions of type IIB supergravity that consist of a warped product of AdS_3 with a seven-dimensional internal space. In one duality frame the only other non-vanishing fields are the NS three-form and the dilaton. We analyse in detail how these local solutions can be extended to globally well-defined solutions of type IIB string theory, with the internal space having topology S^3 x S^3 x S^1 and with properly quantised three-form flux.

Paper Structure

This paper contains 16 sections, 180 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The $AdS_3$ solutions
  3. The local solutions
  4. $B_4=S^2\times S^2$
  5. $M_5=S^3\times S^2$
  6. $M_6=S^3\times S^3$
  7. A quotient of $M_6$ and integral three-forms
  8. Flux Quantisation and the Central Charge
  9. Electric and magnetic charges
  10. Computing periods using coordinate patches
  11. Taking the limit $Q\to 0$
  12. More general identifications
  13. Final Comments
  14. $U(1)$ bundles over Lens spaces
  15. More on the topology of $M_5$
  16. ...and 1 more sections

Figures (1)

  • Figure 1: Desingularisation of $\Sigma_2\cup -\Sigma_f$.