<p>We study timelike supersymmetric solutions of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mo>=</mo><mn>3</mn></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>=</mo><mn>4</mn></mrow></math> gauged supergravity using the Killing spinor bilinears method and prove that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> is the only solution within this class. We then consider the ungauged version of this model. It is found that for this type of solution, the ungauged theory effectively truncates to a supergravity coupled to a sigma model with a two-dimensional hyperbolic target space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="double-struck">H</mi><mn>2</mn></msup></math>, and all solutions can be expressed in terms of two arbitrary holomorphic functions. The spacetime metric is a warped product of the time direction with a two-dimensional space, and the warp factor is given in terms of the Kähler potential of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="double-struck">H</mi><mn>2</mn></msup></math>. We show that when the holomorphic function that determines the sigma model scalar fields is not constant, the metric on the sigma model target manifold becomes part of the spacetime metric. We then look at some special choices for these holomorphic functions for which the spacetime metric and the Killing spinors are only radial dependent. We also derive supersymmetric null solutions of the ungauged model which are pp-waves on the Minkowski spacetime.</p>

Türkiye

Austria

Nihat Sadik Deger

Ceren Ayse Deral

Timelike supersymmetric solutions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo>=</mo><mn>3</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>4</mn></math> supergravity

Minimal massive supergravity is the supersymmetric extension of minimal massive gravity in three dimensions. The theory admits a supersymmetric anti-de Sitter vacuum around which the propagating modes of spin 2 and 3/2 combine into a supermultiplet. In this letter, we determine the most general supersymmetric solution of the theory by analyzing its Killing spinor equations. Just as for topologically massive supergravity, the general supersymmetric solution is a plane wave with a null Killing vector field. As a particular subclass we find null-warped AdS$_{3}$ spaces and, with proper periodic identifications, null-warped AdS$_{3}$ black holes.

Croatia

Jan Rosseel

France

Henning Samtleben

The general supersymmetric solution of minimal massive supergravity

In six dimensions there exists a unique one-parameter family of nonlinear conformal electrodynamics for a chiral 2-form gauge field that includes (in a free-field limit) the linear chiral 2-form theory and is related, by dimensional reduction, to the four-dimensional ModMax electrodynamics. In this work, we present the first exact solutions of this theory in presence of gravity. In particular, we will consider plane wave, Robinson-Trautman, and self-dual dyonic string configurations, generalizing well-known solutions of this type in six-dimensional supergravities with linear chiral 2-form multiplets.

Italy

Ángel J. Murcia

Dmitri Sorokin

Waves and strings in an interacting conformal chiral 2-form theory in six dimensions

We present an action for minimal massive gravity (MMG) in three dimensions in terms of a dreibein and an independent spin connection. Furthermore, the construction provides an action principle for an infinite family of so-called third-way consistent generalizations of the three-dimensional Einstein field equations, including exotic massive gravity and new higher-order generalizations. It allows us to systematically construct the matter couplings for these models, including the couplings to fermions, depending on the spin connection. In particular, we construct different supersymmetric extensions of MMG, and derive their second order fermionic field equations. This establishes a new class of three-dimensional supergravity theories and we discuss their limit to topological massive supergravity. Finally, we identify the landscape of (anti–)de Sitter vacua of the supersymmetric models. We analyze the spectrum and the unitarity properties of these vacua. We recover the known AdS vacua of MMG which are bulk and boundary unitary.

Marc Geiller

Minimal massive supergravity and new theories of massive gravity

Minimal massive gravity in three dimensions propagates a single massive spin-2 mode around an anti–de Sitter vacuum. It is distinguished by allowing for vacua with positive central charges of the asymptotic conformal algebra and a bulk graviton of positive energy. We present a new action for the model (and its higher order extensions) in terms of a dreibein and an independent spin connection. From this, we construct its supersymmetric extension. Surprisingly, all vacua complying with bulk and boundary unitarity appear to break supersymmetry spontaneously. In contrast, all supersymmetric vacua have a negative central charge whenever the bulk graviton has positive energy.

Minimal Massive Supergravity

Three-dimensional Yang-Mills theory allows for a deformation quadratic in the field strengths which can not be integrated to a local action without auxiliary fields. Yet, its covariant divergence consistently vanishes after iterating the equation, realizing a spin-1 analogue of ‘minimal massive gravity’, which has been dubbed ‘third way consistent’. In this note, we show that after dualization of the three-dimensional gauge fields, the model possesses a natural action as a Chern-Simons coupled gauged sigma model. In this dual formulation, coupling to matter and to gravity becomes straightforward. As a direct application, we derive the coupling of the model to <math><mi>N</mi><mo>=</mo><mn>1</mn></math> supergravity.

A note on the third way consistent deformation of Yang-Mills theory

We develop a procedure to reproduce the ten-dimensional generalized supergravity equations from T-duality covariant equations that facilitates generalization to U-duality covariant formulations of eleven-dimensional supergravity. The latter leads to a modification of the eleven-dimensional supergravity equations with terms that contain a rank-2 tensor field, which is the eleven-dimensional analog of the nonunimodularity Killing vector <math><msup><mi>I</mi><mi>m</mi></msup></math> in ten dimensions.

Russia

Ilya Bakhmatov

Aybike Catal-Ozer

Kirill Gubarev

Edvard T. Musaev

Generalizing eleven-dimensional supergravity

We construct three-dimensional, <math><mi>N</mi><mo>=</mo><mn>1</mn></math> off-shell supersymmetric massive Yang-Mills (YM) theory whose YM equation is “third-way” consistent. This means that the field equations of this model do not come from variation of a local action without additional fields, yet the gauge-covariant divergence of the YM equation still vanishes on shell. To achieve this, we modify the massive Majorana spinor equation so that its supersymmetry variation gives a modified YM equation whose bosonic part coincides with the third-way consistent pure massive YM model.

Novel 3D supersymmetric massive Yang-Mills theory

We construct a class of interacting (<math><mrow><mi>d</mi><mo>−</mo><mn>2</mn></mrow></math>)-form theories in <math><mi>d</mi></math> dimensions that are “third-way” consistent. This refers to the fact that the interaction terms in the <math><mi>p</mi></math>-form field equations of motion neither come from the variation of an action nor are they off-shell conserved on their own. Nevertheless, the full equation is still on-shell consistent. Various generalizations, e.g., coupling them to (<math><mrow><mi>d</mi><mo>−</mo><mn>3</mn></mrow></math>)-forms, where three algebras play a prominent role, are also discussed. The method to construct these models also easily recovers the modified three-dimensional Yang-Mills theory obtained earlier and straightforwardly allows for higher derivative extensions.

Germany

Matteo Broccoli

Stefan Theisen

Third Way to Interacting <math><mrow><mi>p</mi></mrow></math>-Form Theories

We construct time and radial dependent solutions that describe p-branes in chargeless S-brane backgrounds. In particular, there are some new M5- and D3-branes among our solutions which have AdS limits and contain a cosmological singularity as well. We also find a time-dependent version of the dyonic membrane configuration in 11-dimensions by applying a Lunin–Maldacena deformation to our new M5-brane solution.