Modular curves and the refined distance conjecture

We test the refined distance conjecture in the vector multiplet moduli space of 4D $$ \mathcal{N} $$ N = 2 compactifications of the type IIA string that admit a dual heterotic description. In the weakly coupled regime of the heterotic string, the moduli space geometry is governed by the perturbative heterotic dualities, which allows for exact computations. This is reflected in the type IIA frame through the existence of a K3 fibration. We identify the degree d = 2N of the K3 fiber as a parameter that could potentially lead to large distances, which is substantiated by studying several explicit models. The moduli space geometry degenerates into the modular curve for the congruence subgroup Γ0(N)+. In order to probe the large N regime, we initiate the study of Calabi-Yau threefolds fibered by general degree d > 8 K3 surfaces by suggesting a construction as complete intersections in Grassmann bundles.

Superconformal duality-invariant models and $$ \mathcal{N} $$ = 4 SYM effective action

We present $$ \mathcal{N} $$ N = 2 superconformal U(1) duality-invariant models for an Abelian vector multiplet coupled to conformal supergravity. In a Minkowski background, such a nonlinear theory is expected to describe (the planar part of) the low-energy effective action for the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills (SYM) theory on its Coulomb branch where (i) the gauge group SU(N) is spontaneously broken to SU(N − 1) × U(1); and (ii) the dynamics is captured by a single $$ \mathcal{N} $$ N = 2 vector multiplet associated with the U(1) factor of the unbroken group. Additionally, a local U(1) duality-invariant action generating the $$ \mathcal{N} $$ N = 2 super-Weyl anomaly is proposed. By providing a new derivation of the recently constructed U(1) duality-invariant $$ \mathcal{N} $$ N = 1 superconformal electrodynamics, we introduce its SL(2, ℝ) duality-invariant coupling to the dilaton-axion multiplet.

Wrapped NS5-branes, consistent truncations and Inönü-Wigner contractions

We construct consistent Kaluza-Klein truncations of type IIA supergravity on (i) Σ2 × S3 and (ii) Σ3 × S3, where Σ2 = S2/Γ, ℝ2/Γ, or ℍ2/Γ, and Σ3 = S3/Γ, ℝ3/Γ, or ℍ3/Γ, with Γ a discrete group of symmetries, corresponding to NS5-branes wrapped on Σ2 and Σ3. The resulting theories are a D = 5, $$ \mathcal{N} $$ N = 4 gauged supergravity coupled to three vector multiplets with scalar manifold SO(1, 1) × SO(5, 3)/(SO(5) × SO(3)) and gauge group SO(2) × (SO(2) $$ {\ltimes}_{\Sigma_2} $$ ⋉ Σ 2 ℝ4) which depends on the curvature of Σ2, and a D = 4, $$ \mathcal{N} $$ N = 2 gauged supergravity coupled to one vector multiplet and two hypermultiplets with scalar manifold SU(1, 1)/U(1) × G2(2)/SO(4) and gauge group ℝ+ × ℝ+ for truncations (i) and (ii) respectively. Instead of carrying out the truncations at the 10-dimensional level, we show that they can be obtained directly by performing Inönü-Wigner contractions on the 5 and 4-dimensional gauged supergravity theories that come from consistent truncations of 11-dimensional supergravity associated with M5-branes wrapping Σ2 and Σ3. This suggests the existence of a broader class of lower-dimensional gauged supergravity theories related by group contractions that have a 10 or 11-dimensional origin.

Superspace first order formalism, trivial symmetries and electromagnetic interactions of linearized supergravity

We introduce a first order description of linearized non-minimal (n = −1) supergravity in superspace, using the unconstrained prepotential superfield instead of the conventionally constrained super one forms. In this description, after integrating out the connection-like auxiliary superfield of first-order formalism, the superspace action is expressed in terms of a single superfield which combines the prepotential and compensator superfields. We use this description to construct the supersymmetric cubic interaction vertex 3/2 − 3/2 − 1/2 which describes the electromagnetic interaction between two non-minimal supergravity multiplets (superspin Y = 3/2 which contains a spin 2 and a spin 3/2 particles) and a vector multiplet (superspin Y = 1/2 contains a spin 1 and a spin 1/2 particles). Exploring the trivial symmetries emerging between the two Y = 3/2 supermultiplets, we show that this cubic vertex must depend on the vector multiplet superfield strength. This result generalize previous results for non-supersymmetric electromagnetic interactions of spin 2 particles. The constructed cubic interaction generates non-trivial deformations of the gauge transformations.

BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

We consider the expectation value $$ \left\langle \mathcal{W}\right\rangle $$ W of the circular BPS Wilson loop in $$ \mathcal{N} $$ N = 2 superconformal SU(N) gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to $$ \mathcal{N} $$ N = 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS5× S5 superstring theory. On the string theory side $$ \left\langle \mathcal{W}\right\rangle $$ W is represented by the path integral expanded near the same AdS2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in [5], we suggest that as in the $$ \mathcal{N} $$ N = 4 SYM case and in the $$ \mathcal{N} $$ N = 2 SU(N) × SU(N) superconformal quiver theory discussed in [19], the coefficient of the leading non-planar 1/N2 correction in $$ \left\langle \mathcal{W}\right\rangle $$ W should have the universal λ3/2 scaling at large ’t Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for $$ \left\langle \mathcal{W}\right\rangle $$ W . We complement the analytic derivation of the λ3/2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.

Distributions of extremal black holes in Calabi-Yau compactifications

We study non-supersymmetric extremal black hole excitations of 4d $$ \mathcal{N} $$ N = 2 supersymmetric string vacua arising from compactification on Calabi-Yau threefolds. The values of the (vector multiplet) moduli at the black hole horizon are governed by the attractor mechanism. This raises natural questions, such as “what is the distribution of attractor points on moduli space?” and “how many attractor black holes are there with horizon area up to a certain size?” We employ tools developed by Denef and Douglas [1] to answer these questions.

Four-dimensional vector multiplets in arbitrary signature (II)

Following the classification up to isomorphism of [Formula: see text] Poincaré Lie superalgebras in four dimensions with arbitrary signature obtained in a companion paper, we present off-shell vector multiplet representations and invariant Lagrangians realizing these algebras. By dimensional reduction of five-dimensional off-shell vector multiplets, we obtain two representations in each four-dimensional signature. In Euclidean and neutral signature, these representations can be mapped to each other by a field redefinition induced by the action of the Schur group on the space of superbrackets. In Minkowski signature, we show that the superbrackets underlying the two vector multiplet representations belong to distinct open orbits of the Schur group and are therefore inequivalent. Our formalism allows to answer questions about the possible relative signs between terms in the Lagrangian systematically by relating them to the underlying space of superbrackets.

New Kähler invariant Fayet–Iliopoulos terms in supergravity and cosmological applications

Recently, a new type of constant Fayet–Iliopoulos (FI) terms was introduced in $${\mathcal {N}}=1$$ N = 1 supergravity, which do not require the gauging of the R-symmetry. We revisit and generalise these constructions, building a new class of Kähler invariant FI terms parametrised by a function of the gravitino mass as functional of the chiral superfields, which is then used to describe new models of inflation. They are based on a no-scale supergravity model of the inflaton chiral multiplet, supplemented by an abelian vector multiplet with the new FI-term. We show that the inflaton potential is compatible with the CMB observational data, with a vacuum energy at the minimum that can be tuned to a tiny positive value. Finally, the axionic shift symmetry can be gauged by the U(1) which becomes massive. These models offer a mechanism for fixing the gravitino mass in no-scale supergravities, that corresponds to a flat direction of the scalar potential in the absence of the new FI-term; its origin in string theory is an interesting open problem.

Lifshitz-type gauge theory with 𝒩 = 2 supersymmetry

We construct an [Formula: see text] supersymmetric gauge theory in Lifshitz space–time. Starting with [Formula: see text] supersymmetric Lagrangian, we introduce an additional [Formula: see text] symmetry between specific component fields. The resultant Lagrangian is shown to have an extra set of supersymmetry, thus realizing an on-shell [Formula: see text] supersymmetric gauge theory. Just as in the case of [Formula: see text], the superderivatives and superfields involved contain higher-order derivatives of spatial coordinates. The constructed [Formula: see text] supersymmetric Lagrangian has both vector multiplet and hypermultiplet.