Global properties of the conformal manifold for S-fold backgrounds

Abstract

We study a one-parameter family of $$ \mathcal{N} $$ N = 2 anti-de Sitter vacua with U(1)2 symmetry of gauged four-dimensional maximal supergravity, with dyonic gauge group [SO(6) × SO(1, 1)] ⋉ ℝ12. These backgrounds are known to correspond to Type IIB S-fold solutions with internal manifold of topology S1 × S5. The family of AdS4 vacua is parametrized by a modulus χ. Although χ appears non-compact in the four-dimensional supergravity, we show that this is just an artefact of the four-dimensional description. We give the 10-dimensional geometric interpretation of the modulus and show that it actually has periodicity of $$ \frac{2\pi }{T} $$ 2 π T , which is the inverse radius of S1. We deduce this by providing the explicit D = 10 uplift of the family of vacua as well as computing the entire modulus-dependent Kaluza-Klein spectrum as a function of χ. At the special values χ = 0 and χ = $$ \frac{\pi }{T} $$ π T , the symmetry enhances according to U(1)2 → U(2), giving rise however to inequivalent Kaluza-Klein spectra. At χ = $$ \frac{\pi }{T} $$ π T , this realizes a bosonic version of the “space invaders” scenario with additional massless vector fields arising from formerly massive fields at higher Kaluza-Klein levels.

The spectrum of marginally-deformed $$ \mathcal{N} $$ = 2 CFTs with AdS4 S-fold duals of type IIB

“…The gauged supergravity is blind to these global features, JHEP12(2021)214 which therefore must be instilled upon the spectra by the uplifted S-folds themselves. Similar observations have already been made in [11]. In order to give further evidence of the relation of the global features of the CM and the uplifted S-folds we determine, in section 4, the type IIB uplift of a notable subset of vacua in the class at hand.…”

“…The periodicity in χ cannot be seen at the D = 4 gauged supergravity level: it is an intrinsically higher-dimensional feature of the corresponding type IIB S-folds, see section 4. The periodicity of χ is already present in the KK spectra, as discussed in [11] and section 3 below. Thus, the large-N CM has one closed one-dimensional boundary, corresponding to the circumference parameterised by χ located at the higher endpoint of the ϕ range in (2.5).…”

“…Again, only the n = 0 realisation is visible in gauged supergravity, and corresponds to the N = 2 SU(2) × U(1) critical point found in [27]; the symmetry enhancement for |n | ≥ 1 can only be seen with a KK analysis [11]. The second such enhancement occurs at .11) and has no counterpart in gauged supergravity [11] of other notable loci within the CM are the following one-parameter families. The following locus parameterised by ϕ,…”

“…R , so that if p, q, y 0 are U(1) a , U(1) b , U(1) R charges, then y 0 = 1 3 (p − q). The SO( 6) in (2.7) and (2.8) is in turn embedded inside the SU(8) compact subgroup of the N = 8 supergravity scalar manifold as the SO(6) v subgroup of the real subgroup SO(8) of SU (8) [11,32]. The commutant of SO (6) v inside SO(8) will be denoted below as SO(2): this is the group that rotates the internal S 1 in the type IIB geometry.…”

“…For this type of AdS solutions, new powerful techniques [1][2][3] based on exceptional field theory (ExFT) [4,5] have been introduced to compute the spectrum of Kaluza-Klein (KK) excitations, dual to the spectrum of operators of the corresponding CFT. These new ExFT-based KK spectral techniques have now been employed in a variety of cases [6][7][8][9][10][11][12].…”