STU Model Research Articles

Euclidean flows, solitons, and wormholes in AdS space from M-theory

Multiparametric families of nonsupersymmetric EAdS4 flows as well as asymptotically EAdS4 solitons and wormholes are constructed within the four-dimensional SO(8) gauged supergravity that describes the compactification of M-theory on S7. More concretely, the solutions are found within the so-called STU model that describes the U(1)4 invariant sector of the theory. The on-shell action and gravitational free energy are computed for the regular solutions, the latter being zero for the wormholes irrespective of supersymmetry. There are special loci in parameter space yielding solutions with enhanced (super)symmetry. Examples include a supersymmetric EAdS4 flow with SO(4)×SO(4) symmetry dual to a specific real mass deformation of ABJM on S3 as well as a nonsupersymmetric wormhole with SU(3)×U(1)2 symmetry. Uplift formulas for these and other examples to Euclidean solutions of 11-dimensional supergravity are presented and their complex nature discussed. Published by the American Physical Society 2024

Supersymmetric solitons in gauged mathcal{N} = 8 supergravity

We consider soliton solutions in AdS4 with a flat slicing and Wilson loops around one cycle. We study the phase structure and find the ground state and identify supersymmetric solutions as a function of the Wilson loops. We work in the context of a scalar field truncation of gauged mathcal{N} = 8 supergravity, where all the dilatons are equal and all the axions vanish in the STU model. In this theory, we construct new soliton solutions parameterized by two Wilson lines. We find that there is a degeneracy of supersymmetric solutions. We also show that, for alternate boundary conditions, there exists a non-supersymmetric soliton solution with energy lower than the supersymmetric one.

The dark (BPS) side of thermodynamics in Minkowski4

We explore the BPS limit of asymptotically flat black hole thermodynamics, drawing analogies with recent studies of black holes in anti-de Sitter space. Although ultimately motivated by supersymmetry and quantum gravity, the BPS limit is classically well-defined for the dyonic Kerr-Newman black holes in pure Einstein-Maxwell theory and various generalizations with additional scalars and gauge fields that admit embedding in mathcal{N} = 2 supergravity (for concreteness we consider the STU model). This limit is manifestly different from extremality as it includes a family of rotating Euclidean saddles that represent a (fictitious) thermal branch, smoothly connected with the extremal static Reissner-Nordström black hole and its generalizations with extra matter. We are able to evaluate unambiguously all BPS chemical potentials, finding constant imaginary angular velocity as a consequence of Wick rotation. In the mixed ensemble of fixed magnetic and varying electric charges, we derive the OSV formula that is crucial for the microscopic understanding of the system, and provide evidence that it should be interpreted as a fixed-point formula.

Classification of four-rebit states

We classify states of four rebits, that is, we classify the orbits of the group Gˆ(R)=SL(2,R)4 in the space (R2)⊗4. This is the real analogon of the well-known SLOCC operations in quantum information theory. By constructing the Gˆ(R)-module (R2)⊗4 via a Z/2Z-grading of the simple split real Lie algebra of type D4, the orbits are divided into three groups: semisimple, nilpotent and mixed. The nilpotent orbits have been classified in Dietrich et al. (2017) [26], yielding applications in theoretical physics (extremal black holes in the STU model of N=2,D=4 supergravity, see Ruggeri and Trigiante (2017) [51]). Here we focus on the semisimple and mixed orbits which we classify with recently developed methods based on Galois cohomology, see Borovoi et al. (2021) [8,9]. These orbits are relevant to the classification of non-extremal (or extremal over-rotating) and two-center extremal black hole solutions in the STU model.

Black hole attractors and U(1) Fayet-Iliopoulos gaugings: analysis and classification

We classify the critical points of the effective black hole potential which governs the attractor mechanism taking place at the horizon of static dyonic extremal black holes in mathcal{N} = 2, D = 4 Maxwell-Einstein supergravity with U(1) Fayet-Iliopoulos gaugings. We use a manifestly symplectic covariant formalism, and we consider both spherical and hyperbolic horizons, recognizing the relevant sub-classes to which some representative examples belong. We also exploit projective special Kähler geometry of vector multiplets scalar manifolds, the U-duality-invariant quartic structure (and 2-polarizations thereof) in order to retrieve and generalize various expressions of the entropy of asymptotically AdS4 BPS black holes, in the cases in which the scalar manifolds are symmetric spaces. Finally, we present a novel static extremal black hole solution to the STU model, in which the dilaton interpolates between an hyperbolic near-horizon geometry and AdS4 at infinity.

Abstract 10258: Do Statins Impact Long-term Mortality Peripheral Artery Disease Patients Who Have End Stage Renal Disease?

Introduction: Statins have shown mortality benefit in peripheral artery disease (PAD), their impact in end-stage renal disease (ESRD) patients with PAD is not well studied. Hypothesis: Does statin utilization have any impact on mortality in ESRD patients with PAD? Methods: We included ESRD Medicare beneficiaries from the United states Renal Database (Jan 1 st 2006 to May 31 st 2017) with PAD within 6 months of incident dialysis. Medicare part D claims were used to determine STU during the follow-up period. Fractional polynomial regression across varying % of STU was generated to predict 2-year mortality. Results: Out of 45,424 ESRD patients with PAD, 62.3% received no statins while the rest had at least some duration of STU. ST was bimodally distributed, with median utilization of 0% (IQR= 0-90%). Mortality was 41.7% over a median follow-up of 472 days. Univariate association of STU on mortality yielded odds ratio (OR) of 0.99 (95% CI = 0.992-0.993; p<0.001). Model 1 including baseline demographics and comorbidities (age, sex, body mass index, hypertension, coronary artery disease, stroke, smoking, diabetes, and heart failure) an AUC of 0.65. The addition of STU (Model 2) resulted in only minimal improvement in the AUC (0.65 vs 0.67; p<0.01). Conclusions: Statin utilization in ESRD patients is associated with only borderline statistically significant reduction in mortality (≈0.1%) of unclear clinical implications

The topologically twisted index of mathcal{N} = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail

We investigate the large-N asymptotics of the topologically twisted index of mathcal{N} = 4 SU(N) Super-Yang-Mills (SYM) theory on T2 × S2 and provide its holographic interpretation based on the black hole Farey tail [1]. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of mathcal{N} = 4 SYM theory as a discrete sum over Bethe vacua, to compute the large-N asymptotics of the twisted index. In a dual mathcal{N} = 2 gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-N limit. This extends the previous microstate counting of an AdS5 black string by the twisted index and thereby improves holographic understanding of the twisted index.

New non-extremal and BPS hairy black holes in gauged mathcal{N} = 2 and mathcal{N} = 8 supergravity

In this article we study a family of four-dimensional, mathcal{N} = 2 supergravity theories that interpolates between all the single dilaton truncations of the SO(8) gauged mathcal{N} = 8 supergravity. In this infinitely many theories characterized by two real numbers — the interpolation parameter and the dyonic “angle” of the gauging — we construct non-extremal electrically or magnetically charged black hole solutions and their supersymmetric limits. All the supersymmetric black holes have non-singular horizons with spherical, hyperbolic or planar topology. Some of these supersymmetric and non-extremal black holes are new examples in the mathcal{N} = 8 theory that do not belong to the STU model. We compute the asymptotic charges, thermodynamics and boundary conditions of these black holes and show that all of them, except one, introduce a triple trace deformation in the dual theory.

Bhargava’s cube and black hole charges

Black holes in a class of string compactifications, known as STU models, carry four electric and four magnetic charges. Furthermore, a duality group, given by the product of three congruence subgroups of SL(2,\({{\mathbb {Z}}}\)), acts on these integer valued charges. By placing these eight charges at the eight corners of a Bhargava cube, we provide a classification of the duality orbits in these theories.

Euclidean black saddles and AdS4 black holes

We find new asymptotically locally AdS4 Euclidean supersymmetric solutions of the STU model in four-dimensional gauged supergravity. These “black saddles” have an S1× {Sigma}_{mathfrak{g}} boundary at asymptotic infinity and cap off smoothly in the interior. The solutions can be uplifted to eleven dimensions and are holographically dual to the topologically twisted ABJM theory on S1× {Sigma}_{mathfrak{g}} . We show explicitly that the on-shell action of the black saddle solutions agrees exactly with the topologically twisted index of the ABJM theory in the planar limit for general values of the magnetic fluxes, flavor fugacities, and real masses. This agreement relies on a careful holographic renormalization analysis combined with a novel UV/IR holographic relation between supergravity parameters and field theory sources. The Euclidean black saddle solution space contains special points that can be Wick-rotated to regular Lorentzian supergravity backgrounds that correspond to the well-known supersymmetric dyonic AdS4 black holes in the STU model.

An approach to BPS black hole microstate counting in an N = 2 STU model

We consider four-dimensional dyonic single-center BPS black holes in the N = 2 STU model of Sen and Vafa. By working in a region of moduli space where the real part of two of the three complex scalars S, T , U are taken to be large, we evaluate the quantum entropy function for these BPS black holes. In this regime, the subleading corrections point to a microstate counting formula partly based on a Siegel modular form of weight two. This is supplemented by another modular object that takes into account the dependence on Y0, a complex scalar field belonging to one of the four off-shell vector multiplets of the underlying supergravity theory. We also observe interesting connections to the rational Calogero model and to formal deformation of a Poisson algebra, and suggest a string web picture of our counting proposal.

Holographic uniformization and black hole attractors

We establish an attractor mechanism for the horizon metric of asymptotically locally AdS4 supersymmetric black holes. The horizon is a smooth Riemann surface with arbitrary metric at asymptotic infinity which is fixed to the constant curvature metric in the near horizon region. We show how this mechanism is realized for four-dimensional mathcal{N} = 2 gauged supergravity coupled to vector multiplets by focusing on the STU model. A similar analysis is performed for gauged supergravity theories in five, six, and seven dimen- sions where we establish the same mechanism by extending previous results on holographic uniformization.

QGP universality in a magnetic field?

We use top-down holographic models to study the thermal equation of state of strongly coupled quark-gluon plasma in external magnetic field. We identify different conformal and non-conformal theories within consistent truncations of mathcal{N} = 8 gauged supergravity in five dimensions (including STU models, gauged mathcal{N} = 2* theory) and show that the ratio of the transverse to the longitudinal pressure PT /PL as a function of T / sqrt{B} can be collapsed to a ‘universal’ curve for a wide range of the adjoint hypermultiplet masses m. We stress that this does not imply any hidden universality in magnetoresponse, as other observables do not exhibit any universality. Instead, the observed collapse in PT /PL is simply due to a strong dependence of the equation of state on the (freely adjustable) renormalization scale: in other words, it is simply a fitting artifact. Remarkably, we do uncover a different universality in mathcal{N} = 2* gauge theory in the external magnetic field: we show that magnetized mathcal{N} = 2* plasma has a critical point at Tcrit/ sqrt{B} which value varies by 2% (or less) as m/ sqrt{B} ∈ [0, ∞). At criticality, and for large values of m/ sqrt{B} , the effective central charge of the theory scales as ∝ sqrt{B} /m.

Mass production of IIA and IIB dS vacua

We describe several applications of the mass production procedure proposed in [1] to stabilize multiple moduli in a dS vacuum, in supergravity models inspired by string theory. The construction involves a small downshift of an initial supersymmetric Minkowski minimum to a supersymmetric AdS minimum, and a consequent small uplift to a dS minimum. Our type IIA examples include dS stabilization in a 7-moduli model with [SL(2, ℝ)]7 tree level symmetry, and its simplified version, a 3-moduli STU model. In these models, we use uplifting anti-D6 branes. In type IIB models, we present 2- and 3-moduli examples of stable dS vacua in CY three-folds, with an uplifting anti-D3 brane. These include K3 fibration models, a CICY model and a multi-hole Swiss cheese model. We also address the issue whether this procedure is limited to a very small parameter range or if large deviations from the progenitor Minkowski vacuum are possible.

Uplifting anti-D6-brane

A simple, KKLT-like construction of de Sitter vacua in type IIA string theory is presented in an STU model with guidance from string theory U-duality and with an up- lifting anti-D6-brane. In four dimensions the model is reduced to mathcal{N} = 1 supergravity with three chiral multiplets, namely S, T and U , as well as one nilpotent multiplet representing the anti-D6-brane. We briefly discuss also a generalization with seven moduli.

Holographic OPE coefficients from AdS black holes with matters

We study the OPE coefficients cΔ, J for heavy-light scalar four-point functions, which can be obtained holographically from the two-point function of a light scalar of some non-integer conformal dimension ΔL in an AdS black hole. We verify that the OPE coefficient cd,0 = 0 for pure gravity black holes, consistent with the tracelessness of the holographic energy-momentum tensor. We then study the OPE coefficients from black holes involving matter fields. We first consider general charged AdS black holes and we give some explicit low-lying examples of the OPE coefficients. We also obtain the recursion formula for the lowest-twist OPE coefficients with at most two current operators. For integer ΔL, although the OPE coefficients are not fully determined, we set up a framework to read off the coefficients γΔ,J of the log(z overline{z} ) terms that are associated with the anomalous dimensions of the exchange operators and obtain a general formula for γΔ,J. We then consider charged AdS black holes in gauged supergravity STU models in D = 5 and D = 7, and their higher-dimensional generalizations. The scalar fields in the STU models are conformally massless, dual to light operators with ΔL = d − 2. We derive the linear perturbation of such a scalar in the STU charged AdS black holes and obtain the explicit OPE coefficient cd−2,0. Finally, we analyse the asymptotic properties of scalar hairy AdS black holes and show how cd,0 can be nonzero with exchanging scalar operators in these backgrounds.

Generating new N = 2 small black holes

We use the exact symmetries of the N = 2 STU model of Sen and Vafa to classify BPS orbits in this theory. Subsequently, we construct examples of small BPS black holes in this model by solving the associated attractor equations, and use duality symmetries as a solution generating technique to construct a two-center bound state of small BPS black holes in asymptotically flat space-time.

AdS5 black strings in the stu model of FI-gauged N = 2 supergravity

We analytically construct asymptotically AdS5 black string solutions starting from the four-dimensional domain wall black hole of [1]. It is shown that its uplift gives a black string in d = 5 minimal gauged supergravity, with momentum along the string. Applying instead the residual symmetries of N = 2, d = 4 Fayet-Iliopoulos-gauged super-gravity discovered in [2] to the domain wall seed leads, after uplifting, to a dyonic black string that interpolates between AdS5 and AdS3 × H2 at the horizon. A Kaluza-Klein reduction of the latter along an angular Killing direction ϕ followed by a duality transformation yields, after going back to five dimensions, a black string with both momentum along the string and rotation along ϕ. This is the first instance of using solution-generating techniques in gauged supergravity to add rotation to a given seed. These solutions all have constant scalar fields. As was shown in [3], the construction of supersymmetric static magnetic black strings in the FI-gauged stu model amounts to solving the SO(2, 1) spinning top equations, which descend from an inhomogeneous version of the Nahm equations. We are able to solve these in a particular case, which leads to a generalization of the Maldacena-Nuñez solution.

Holographic superconductor in a deformed four-dimensional STU model

In this paper, we consider a deformed STU model in four dimensions including both electric and magnetic charges. Using the AdS/CFT correspondence, we study holographic superconductors and obtain transport properties like electrical and thermal conductivities. We obtain transport properties in terms of the magnetic charge of the black hole and interpret it as the magnetic monopole of dual field theory. We find that the presence of the magnetic charge is necessary to have maximum conductivities, and the existence of a magnetic monopole with a critical charge (137 e) to reach the maximum superconductivity is important. Also, we show that the thermal conductivity increases with increasing of the magnetic charge. It may be concluded that the origin of superconductivity is the magnetic monopole.

Non-geometric Calabi-Yau backgrounds and K3 automorphisms

We consider compactifications of type IIA superstring theory on mirror-folds obtained as K3 fibrations over two-tori with non-geometric monodromies involving mirror symmetries. At special points in the moduli space these are asymmetric Gepner models. The compactifications are constructed from non-geometric automorphisms that arise from the diagonal action of an automorphism of the K3 surface and of an automorphism of the mirror surface. We identify the corresponding gaugings of mathcal{N} = 4 supergravity in four dimensions, and show that the minima of the potential describe the same four-dimensional low-energy physics as the worldsheet formulation in terms of asymmetric Gepner models. In this way, we obtain a class of Minkowski vacua of type II string theory which preserve mathcal{N} = 2 supersymmetry. The massless sector consists of mathcal{N} = 2 supergravity coupled to 3 vector multiplets, giving the STU model. In some cases there are additional massless hypermultiplets.