Massive Type IIA Research Articles

Spin-2 operators in two-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = (4, 0) quivers from massive type IIA

In this work we revisit the problem of studying spin-2 fluctuations around a class of solutions in massive type IIA that is given by a warped AdS3 × S2 × T4 × Iρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{I}}_{\\rho } $$\\end{document} and with N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = (4, 0) supersymmetry. We were able to identify a class of fluctuations, which is known as the “minimal universal class” that is independent of the background data and saturates the bound on the mass related to the field theory unitarity bound. These operators have conformal dimension ∆ = 2(ℓ + 1), with ℓ being the quantum number of the angular momentum on the S2. We also computed the normalisation of the 2-point function of stress-energy tensors from the effective 3-dimensional graviton action. We comment on the relation of our results to the related AdS3 and AdS2 solutions in massive type IIA and type IIB theories respectively.

A geometric dual of F-maximization in massive type IIA

Using equivariant localization we construct a geometric dual of F-maximization in massive type IIA supergravity. Our results use only topological data to quantize the fluxes, compute the free-energy and conformal dimensions of operators in the dual field theory without the need for explicit solutions. We utilize our formalism to study various classes of solutions, including examples where an explicit solution is not known.

Holographic 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document}-BPS surface defects in ABJM

We study the class of AdS3 × ℂℙ3 solutions to massive Type IIA supergravity with osp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{osp} $$\\end{document}(6|2) superconformal algebra recently constructed in [1]. These solutions are foliations over an interval preserving N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = (0, 6) supersymmetry in two dimensions, that in the massless limit can be mapped to the AdS4 × ℂℙ3 solution of ABJM/ABJ. We show that in the massive case extra NS5-D8 branes, that we interpret as 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document}-BPS surface defect branes within the ABJ theory, backreact in the geometry and turn one of the 3d field theory directions onto an energy scale, generating a flow towards a 2d CFT. We construct explicit quiver field theories that we propose flow in the IR to the (0, 6) SCFTs dual to the solutions. Finally, we show that the AdS3 solutions realise geometrically, in terms of large gauge transformations, an extension to the massive case of Seiberg duality in ABJ theories proposed in the literature.

G-structures for black hole near-horizon geometries

We derive necessary and sufficient conditions for warped AdS2 solutions of Type II supergravity to preserve N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetry, in terms of bispinors. Such solutions generically support an SU(3)-structure on their internal manifold M8, which can experience an enhancement to a G2-structure. We perform an SU(3)-structure torsion classes analysis and express the fluxes and other physical fields in terms of these, in general. We use our results to derive two new classes of AdS2 solutions. In (massive) Type IIA supergravity we derive an N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetric class for which M8 decomposes as a weak G2-manifold foliated over an interval and which is locally defined in terms of a degree three polynomial. In Type IIB supergravity we find a class of AdS2 × S2 × CY2 × Σ2 solutions preserving small N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 supersymmetry, governed by a harmonic function on Σ2 and partial differential equations reminiscent of D3-D7-brane configurations.

β symmetry in type II supergravities

A non geometric sector of the duality group emerging in Kaluza-Klein reductions is realized as an effective symmetry in the low energy action of uncompactified type II theories. This is achieved by extending the so called β symmetry of the universal NS-NS sector to the R-R sector of type IIA, IIB and massive type IIA.

M5-branes and D4-branes wrapped on a direct product of spindle and Riemann surface

We construct multi-charged AdS3× ⅀ ×Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document} and AdS2× ⅀ ×Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document} solutions from M5-branes and D4-branes wrapped on a direct product of spindle, ⅀, and Riemann surface, Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document}. Employing uplift formula, we obtain these solutions by uplifting the multi-charged AdS3× ⅀ and AdS2× ⅀ solutions to seven and six dimensions, respectively. We further uplift the solutions to eleven-dimensional and massive type IIA supergravity and calculate the holographic central charge and the Bekenstein-Hawking entropy, respectively. We perform the gravitational block calculations and, for the AdS3× ⅀ ×Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document} solutions, the result precisely matches the holographic central charge from the supergravity solutions.

Extensions of a scale-separated AdS4 solution and their mass spectrum

We consider two extensions of the so-called DGKT solution, a 4d scale-separated anti-de Sitter (AdS) solution obtained as a compactification on a 6d torus orbifold. Each extension consists in a specific large n expansion beyond the DGKT solution, where n is the unbounded F4-flux parameter. One of the extensions considered generalizes the known warped, partially backreacted solution. We analyse the two extensions in 10d massive type IIA supergravity as well as in a 4d effective theory, using a general warped compactification formalism, including axions. On top of known corrections to DGKT, we mainly get new ones from F4; other fluxes are very constrained by flux quantization. In each extension, one would expect corresponding corrections to the mass spectrum, before reaching contributions from α′-corrections. But the mass spectrum turns out to be robust, and conformal dimensions remain unchanged.

New families of scale separated vacua

Massive type IIA flux compactifications of the form AdS4 × X6, where X6 admits a Calabi-Yau metric and O6-planes wrapping three-cycles, display families of vacua with parametric scale separation between the compactification scale and the AdS4 radius, generated by an overall rescaling of internal four-form fluxes. For toroidal orbifolds one can perform two T-dualities and map this background to an orientifold of massless type IIA compactified on an SU(3)-structure manifold with fluxes. Via a 4d EFT analysis, we generalise this last construction and embed it into new branches of supersymmetric and non-supersymmetric vacua with similar features. We apply our results to propose new infinite families of vacua based on elliptic fibrations with metric fluxes. Parametric scale separation is achieved by an asymmetric flux rescaling which, however, in general is not a simple symmetry of the 4d equations of motion. At this level of approximation the vacua are stable but, unlike in the Calabi-Yau case, they display a non-universal mass spectrum of light fields.

On/off scale separation

We discuss minimally supersymmetric AdS3 flux vacua of massive type IIA supergravity on G2-orientifolds. We find that configurations with broken scale-separation can be within finite distance from scale-separated ones, while both remain at large volume, weak coupling and have moduli stabilization. The transition is achieved with the use of a D4-brane modulus, which allows the F4 flux to jump, and has an effective potential always accessible to the three-dimensional low-energy theory. Our analysis further allows us to check the distance conjecture quantitatively, as we can track explicitly the masses of the KK modes.

Superstrings on Penrose limits of AdS7 solutions

We consider the Penrose limit of AdS7 solutions of massive Type IIA supergravity. The resulting pp-wave geometry is supported by RR and NSNS fields. We quantize the Green-Schwarz superstring on the obtained pp-wave background, in the light-cone gauge.

Compactification of 6d [formula omitted] quivers, 4d SCFTs and their holographic dual Massive IIA backgrounds

In this paper we study an infinite family of Massive Type IIA backgrounds that holographically describe the twisted compactification of N=(1,0) six-dimensional SCFTs to four dimensions. The analysis of the branes involved motivates an heuristic proposal for a four dimensional linear quiver QFT, that deconstructs the theory in six dimensions. For the case in which the system reaches a strongly coupled fixed point, we calculate some observables that we compare with holographic results. Two quantities measuring the number of degrees of freedom for the flow across dimensions are studied.

Holographic 3d mathcal{N} = 1 conformal manifolds

We construct and study several examples of continuous families of AdS4 mathcal{N} = 1 solutions of four-dimensional maximal gauged supergravity. These backgrounds provide the holographic descriptions of conformal manifolds of the dual 3d mathcal{N} = 1 SCFTs. The solutions we study can be uplifted to type IIB supergravity where they arise from D3-branes wrapping an S1 with an S-duality twist. We find the spectrum of low lying operators in the 3d mathcal{N} = 1 SCFTs as a function of the exactly marginal coupling and discuss the structure of the corresponding superconformal multiplets. Using string theory techniques we also study additional examples of continuous families of mathcal{N} = 1 AdS4 vacua in type IIB and massive type IIA supergravity.

A 10d construction of Euclidean axion wormholes in flat and AdS space

Euclidean wormhole geometries sourced by axions and dilatons are puzzling objects in quantum gravity. From one side of the wormhole to the other, the scalar fields traverse a few Planck lengths in field space and so corrections from the UV might potentially affect the consistency of the solution, even when the wormholes are large. Motivated by this, we carry out the first explicit 10d lifts of regular Euclidean axion wormholes. We start off with the lift of Giddings-Strominger wormholes in mathcal{N} = 8 Euclidean supergravity over a 6-torus to 10d type IIA supergravity and find the solution can be everywhere tuned into the parametrically controlled supergravity regime. Secondly, we construct explicit wormholes in AdS spaces and find them again to be under parametric control. We find the first wormhole solutions in massive type IIA on S3 × S3 and in type IIB on T1,1. The latter has an explicit holographic dual, and similar to the earlier constructions in AdS5 × S5/ℤk, the wormholes violate operator positivity since Tr(F ± ⋆ F)2< 0. This puzzle might arise from subtleties related to computing holographic n-point functions in the presence of multiple boundaries.

D4-branes wrapped on a topological disk

Employing the method applied to M5-branes recently by Bah, Bonetti, Minasian and Nardoni, we study D4-branes wrapped on a disk with a non-trivial holonomy at the boundary. In F (4) gauged supergravity in six dimensions, we find supersymmetric AdS4 solutions and uplift the solutions to massive type IIA supergravity. We calculate the holographic free energy of dual three-dimensional superconformal field theories.

A quantum mechanics for magnetic horizons

We construct an mathcal{N} = 2 supersymmetric gauged quantum mechanics, by starting from the 3d Chern-Simons-matter theory holographically dual to massive Type IIA string theory on AdS4× S6, and Kaluza-Klein reducing on S2 with a background that is dual to the asymptotics of static dyonic BPS black holes in AdS4. The background involves a choice of gauge fluxes, that we fix via a saddle-point analysis of the 3d topologically twisted index at large N. The ground-state degeneracy of the effective quantum mechanics reproduces the entropy of BPS black holes, and we expect its low-lying spectrum to contain information about near-extremal horizons. Interestingly, the model has a large number of statistically-distributed couplings, reminiscent of SYK models.

Branes wrapped on orbifolds and their gravitational blocks

We construct new supersymmetric textrm{AdS}_2times mathbb {M}_4 solutions of D=6 gauged supergravity, where mathbb {M}_4 are certain four-dimensional orbifolds. After uplifting to massive type IIA supergravity these correspond to the near-horizon limit of a system of N D4-branes and N_f D8-branes wrapped on mathbb {M}_4. In one class of solutions, is a spindle fibered over a smooth Riemann surface of genus textrm{g}>1, while in another class is a spindle fibered over another spindle. Both classes can be thought of as orbifold generalizations of Hirzebruch surfaces and, in the second case, we describe the solutions in terms of toric geometry. We show that the entropy associated with these solutions is reproduced by extremizing an entropy function obtained by gluing gravitational blocks, using a general recipe for orbifolds that we propose. We also discuss how our prescription can be used to define an off-shell central charge whose extremization reproduces the gravitational central charge of analogous textrm{AdS}_3times mathbb {M}_4 solutions of D=7 gauged supergravity, arising from wrapping M5-branes on mathbb {M}_4.

Hierarchies of RG flows in 6d (1, 0) massive E-strings

We extend the analysis of [9] to the 6d (1, 0) SCFTs known as massive E-string theories, which can be engineered in massive Type IIA with 8 − n0< 8 D8-branes close to an O8− (or O8* if n0 = 8, 9). For each choice of n0 = 1, …, 9 the massive {E}_{1+left(8-{n}_0right)} -strings (including the more exotic {overset{sim }{E}}_1 and E0) are classified by constrained E8 Kac labels, i.e. a subset of Hom(ℤk, E8), from which one can read off the flavor subalgebra of {E}_{1+left(8-{n}_0right)} of each SCFT. We construct hierarchies for two types of Higgs branch RG flows: flows between massive theories defined by the same n0 but different labels; flows between massive theories with different n0. These latter flows are triggered by T-brane vev’s for the right SU factor of the SCFT global symmetry, whose rank is a function of both k and n0, a situation which has so far remained vastly unexplored.

D4-branes wrapped on four-dimensional orbifolds through consistent truncation

We construct a consistent truncation of six-dimensional matter coupled F(4) gauged supergravity on a cornucopia of two-dimensional surfaces including a spindle, disc, domain wall and other novel backgrounds to four-dimensional minimal gauged supergravity. Using our consistent truncation we uplift known AdS2× Σ1 solutions giving rise to four-dimensional orbifold solutions, AdS2× Σ1 ⋉ Σ2. We further uplift our solutions to massive type IIA supergravity by constructing the full uplift formulae for six-dimensional U(1)2-gauged supergravity including all fields and arbitrary Romans mass and gauge coupling. The solutions we construct are naturally interpreted as the near-horizon geometries of asymptotically AdS6 black holes with a four-dimensional orbifold horizon. Alternatively, one may view them as the holographic duals of superconformal quantum mechanical theories constructed by compactifying five-dimensional USp(2N) theory living on a stack of D4-D8 branes on the four-dimensional orbifolds. As a first step to identifying these quantum mechanical theories we compute the Bekenstein-Hawking entropy holographically.

A plethora of Type IIA embeddings for d = 5 minimal supergravity

We construct multiple embeddings of all solutions of d = 5 minimal (un)gauged supergravity into massive Type IIA supergravity. The internal spaces and warpings of such embeddings are the same as those of the mathcal{N} = 1 supersymmetric (Mink5) AdS5 vacua, with the slight modification that the U(1) R-symmetry direction becomes fibered over the external space by the d = 5 gauge field. In addition the fluxes are appropriately modified. There are many distinct types of the aforementioned internal spaces and as such many different embeddings of the d = 5 supergravity. As examples of our setup we provide new solutions dual to six-dimensional, mathcal{N} = (1, 0) SCFTs compactified on the product of a constant curvature Riemann surface and a spindle. We also provide a multitude of massive Type IIA embeddings for rotating, asymptotically AdS5 black hole solutions.

New instabilities for non-supersymmetric AdS4 orientifold vacua

We consider massive type IIA orientifold compactifications of the form AdS4× X6, where X6 admits a Calabi-Yau metric and is threaded by background fluxes. From a 4d viewpoint, fluxes generate a potential whose vacua have been classified, including one mathcal{N} = 1 and three perturbatively stable mathcal{N} = 0 branches. We reproduce this result from a 10d viewpoint, by solving the type IIA equations at the same level of detail as previously done for the mathcal{N} = 1 branch. All solutions exhibit localised sources and parametric scale separation. We then analyse the non-perturbative stability of the mathcal{N} = 0 branches. We consider new 4d membranes, obtained from wrapping D8-branes on X6 or D6-branes on its divisors, threaded by non-diluted worldvolume fluxes. Using them we show that all branches are compatible with the Weak Gravity Conjecture for membranes. In fact, most vacua satisfy the sharpened conjecture that predicts superextremal membranes in mathcal{N} = 0 settings, except for a subset whose non-perturbative stability remains an open problem.