U folds from geodesics in moduli space

• Published in: Physical review. D 2024-04, Vol.109 (8), Article 086018
• Main Authors: Astesiano, D., Ruggeri, D., Trigiante, M.
• Format: Article
• Language: English
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.109.086018

We exploit the presence of moduli fields in the AdS 3 × S 3 × C Y 2 , where C Y 2 = T 4 or K 3 , solution to type IIB superstring theory, to construct a U -fold solution with geometry AdS 2 × S 1 × S 3 × C Y 2 . This is achieved by giving a nontrivial dependence of the moduli fields in SO ( 4 , n ) / SO ( 4 ) × SO ( n ) ( n = 4 for C Y 2 = T 4 and n = 20 for C Y 2 = K 3 ), on the coordinate η of a compact direction S 1 along the boundary of AdS 3 , so that these scalars, as functions of η , describe a geodesic on the corresponding moduli space. The backreaction of these evolving scalars on spacetime amounts to a splitting of AdS 3 into AdS 2 × S 1 with a nontrivial monodromy along S 1 defined by the geodesic. Choosing the monodromy matrix in SO ( 4 , n ; Z ) , this supergravity solution is conjectured to be a consistent superstring background. We generalize this construction starting from an ungauged theory in D = 2 d , d odd, describing scalar fields nonminimally coupled to ( d − 1 ) forms and featuring solutions with topology AdS d × S d , and moduli scalar fields. We show, in this general setting, that giving the moduli fields a geodesic dependence on the η coordinate of an S 1 at the boundary of AdS d is sufficient to split this space into AdS d − 1 × S 1 , with a monodromy along S 1 defined by the starting and ending points of the geodesic. This mechanism seems to be at work in the known J -fold solutions in D = 10 type IIB theory and hints toward the existence of similar solutions in the type IIB theory compactified on C Y 2 . We argue that the holographic dual theory on these backgrounds is a 1 + 0 CFT on an interface in the 1 + 1 theory at the boundary of the original AdS 3 .