We investigate the fully supersymmetric solutions in a class of $$\mathcal{N}=3$$ and $$\mathcal{N}=4$$ higher derivative Poincaré supergravity theories. These class of theories are obtained within the framework of conformal supergravity using the standard Weyl multiplet and contains a set of terms related to the Weyl square term by supersymmetry. We work in the superconformal formalism and show that flat spacetime is the only fully supersymmetric solution in these theories. However, in $$\mathcal{N}=2$$ Poincaré supergravity theories that falls into the same class, two fully supersymmetric stationary solutions exist: Bertotti-Robinson geometry ($\textit{AdS}$ × $\textit{S}$ ) and flat spacetime, which are known in the literature. We discuss the reason behind the richer vacua in $$\mathcal{N}=2$$ supergravity compared to its $$\mathcal{N}=3$$ and $$\mathcal{N}=4$$ cousins.

India

Abhinava Bhattacharjee

Germany

Subramanya Hegde

Bindusar Sahoo

Only flat spacetime is full BPS in four dimensional $$\mathcal{N}=3$$ and $$\mathcal{N}=4$$ supergravity

<p>We construct a new dilaton Weyl multiplet for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>3</mn></math> conformal supergravity in four dimensions. The R-symmetry realized on this dilaton Weyl multiplet is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math>. The construction follows a two-step procedure. First, two on-shell vector multiplets are coupled to the standard Weyl multiplet. Second, using the field equations of the vector multiplets, some of the auxiliary fields of the standard Weyl multiplet are solved in terms of the fields belonging to the vector multiplets and some dual gauge fields. The remaining fields of the standard Weyl multiplet combine with the vector multiplet fields and the dual gauge fields to constitute the new dilaton Weyl multiplet.</p>

Soumya Adhikari

Aravind Aikot

South Korea

Madhu Mishra

Variant dilaton Weyl multiplet for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>3</mn></math> conformal supergravity in four dimensions

We study various $$\mathcal{N}$$ = 2 multiplets in four dimensions by looking at the supersymmetric truncation of four dimensional $$\mathcal{N}$$ = 3 multiplets. Under supersymmetric truncation, the off-shell $$\mathcal{N}$$ = 3 Weyl multiplet reduces to the off-shell $\textit{N}$ = 2 Weyl multiplet and the off-shell $$\mathcal{N}$$ = 2 vector multiplet (which we will refer to as the central charge multiplet). Under the same truncation, the on-shell $$\mathcal{N}$$ = 3 vector multiplet reduces to the on-shell $$\mathcal{N}$$ = 2 vector multiplet and an on-shell massive hypermultiplet with a broken rigid SU(2) and a non-trivial central charge transformation. We use the field equations of this hypermultiplet to eliminate some of the fields of the central charge multiplet in terms of the fields of the hypermultiplet and a dual tensor gauge field (similar in spirit to how a dilaton Weyl multiplet is constructed). This results in a new off-shell matter multiplet, with 8 + 8 degrees of freedom, containing scalar fields and a tensor gauge field, which we refer to as the scalar-tensor multiplet.

Scalar-tensor multiplet in four dimensional $$\mathcal{N}$$ = 2 conformal supergravity

We construct a dilaton Weyl multiplet for $$ \mathcal{N} $$ = 3 conformal supergravity in four dimensions. We couple an on-shell vector multiplet to the standard Weyl multiplet and use the field equations of the vector multiplet to replace some of the components of the auxiliary fields of the standard Weyl multiplet with the fields of the vector multiplet and some dual gauge fields. The R-symmetry of the multiplet is SU(2) × U(1) × U(1). Furthermore, we gauge fix one of the two U(1) symmetries and rewrite the result for the dilaton Weyl multiplet with SU(2) × U(1) R-symmetry.

Dilaton Weyl multiplets for $$ \mathcal{N} $$ = 3 conformal supergravity in four dimensions

New dilaton Weyl multiplets are constructed in four and five space-time dimensions for $\textit{N}$ = 4 and $\textit{N}$ = 2 conformal supergravity respectively. They are constructed from a mixture of the old dilaton weyl multiplets with an on-shell vector multiplet. The old dilaton Weyl multiplets have a USp(4) R-symmetry group whereas the new multiplets have SU(2) × SU(2) R-symmetry, which is a subgroup of USp(4). In six dimensions, for the first time, we construct a dilaton Weyl multiplet for (2, 0) conformal supergravity from a mixture of the standard Weyl multiplet and a tensor multiplet. The R-symmetry group for the dilaton Weyl multiplet in six dimensions is also SU(2) × SU(2).

SU(2) × SU(2) dilaton Weyl multiplets for maximal conformal supergravity in four, five, and six dimensions

We consider the dimensional reduction of N = (2, 0) conformal supergravity in six dimensions on a two-torus to N = 4 conformal supergravity in four dimensions. At the level of kinematics, the six-dimensional Weyl multiplet is shown to reduce to a mixture of the N = 4 Weyl and vector multiplets, which can be reinterpreted as a new off-shell multiplet of N = 4 conformal supergravity. Similar multiplets have been constructed in other settings and are referred to as dilaton Weyl multiplets. We derive it here for the first time in a maximally supersymmetric context in four dimensions. Furthermore, we present the non-linear relations between all the six- and four-dimensional bosonic and fermionic fields, that are obtained by comparing the off-shell supersymmetry transformation rules.

France

Franz Ciceri

Belgium

Axel Kleinschmidt

United Kingdom

Subrabalan Murugesan

Torus reduction of maximal conformal supergravity

<math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 conformal supergravity in five dimensions is constructed via a systematic off-shell reduction scheme from maximal conformal supergravity in six dimensions which is (2, 0). The dimensional reduction of the (2, 0) Weyl multiplet in six dimensions gives us the Weyl multiplet in five dimensions which is a dilaton Weyl multiplet as it has a dilaton scalar. The dimensional reduction of the (2, 0) tensor multiplet in six dimensions gives us the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 vector multiplet in five dimensions coupled to conformal supergravity. We also comment on Nahm’s classification regarding the non-existence of an   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 superconformal algebra in five dimensions and why it does not contradict the existence of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 conformal supergravity in five dimensions that is constructed in this paper.

<math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 conformal supergravity in five dimensions

In this paper we use the superconformal approach to derive the higher derivative action for 𝒩 = 3 Poincaré supergravity in four space-time dimensions. We first study the coupling of 𝒩 = 3 vector multiplets to conformal supergravity. Thereafter we combine it with the pure 𝒩 = 3 conformal supergravity action and use a minimum of three vector multiplets as compensators to arrive at Poincaré supergravity with higher derivative corrections. We give a general prescription on how to eliminate the auxiliary fields in an iterative manner and obtain the supergravity action order by order in derivatives. We also show that the truncation of the action at fourth order in derivatives is a consistent truncation.

Debangshu Mukherjee

Higher derivative invariants in four dimensional 𝒩 = 3 Poincaré supergravity

In this paper we derive the action for N = 3 conformal supergravity in four space-time dimensions. We construct a density formula for N = 3 conformal supergravity based on the superform action principle. Finally, we embed the N = 3 Weyl multiplet in the density formula to obtain the invariant action for N = 3 conformal supergravity. There are two inequivalent embeddings by changing a particular coefficient from real to imaginary. They lead to invariant actions, which will either be the supersymmetrization of the Weyl square term or the Pontryagin density in the eventuality of gauge fixing to Poincaré supergravity. As a consistency check of our formalism, we will show that the supersymmetrization of the Pontryagin density is a total derivative. We will demonstrate this for purely bosonic terms. We will also present the complete action for the supersymmetrization of Weyl square term. We also discuss consistent truncation of N = 4 Weyl multiplet to N = 3 Weyl multiplet and use it for a robust check of our results using the earlier known results in N = 4 conformal supergravity.

N = 3 conformal supergravity in four dimensions

In this paper we derive the most general curvature squared action coupled to an arbitrary number of vector multiplets in four dimensional N = 2 supergravity using the dilaton Weyl multiplet. The action that we derive is encoded in a single holomorphic prepotential.