Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity

Abstract

Candidate counterterms break E7 type U-duality symmetry of $N\ge 5$ supergravity theories in four dimensions \cite{Kallosh:2011dp}. A proposal was made in \cite{Bossard:2011ij} to restore it, starting with a double set of vector fields and argued that a supersymmetric extension of their proposal should exist. We show that the extra vectors, needed for the deformation, can not be auxiliary fields in an eventual off-shell formulation $N\ge 5$ supergravity, assuming that such a formulation exists. Furthermore we show that these extra vector fields can not be dynamical either since that changes the unitary supermultiplets underlying these theories and requires one to go beyond the standard framework of extended simple supergravities. To show this we list all relevant unitary conformal supermultiplets of $SU(2,2|N+n)$. We find that doubling of vectors consistent with linearized supersymmetry requires to change the number of scalars, violating the coset structure of the theory, and also to add a finite number of higher spin fields, which do not admit consistent couplings to theories with spins $\le 2$. Thus, the proposed duality restoring deformation along the lines of \cite{Bossard:2011ij} can not be implemented within the standard framework of extended supergravity theories. We argue therefore that, in the absence of anomalies, E7 type duality together with supersymmetry, might protect $N\ge 5$ supergravity from UV divergences, in particular, $N=5$ supergravity at 4 loops in d=4.

arXiv comment24 p, 8 Tables

References in corpus (45)

• New Goldstone multiplet for partially broken supersymmetry
• Three-Loop Superfiniteness of N=8 Supergravity
• Inconsistency of interacting, multi-graviton theories
• Partial breaking of global D=4 supersymmetry, constrained superfields, and 3-brane actions
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• U-Duality and Central Charges in Various Dimensions Revisited
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• 4D Doubleton Conformal Theories, CPT and IIB String on AdS_5 X S^5
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• New supersymmetric higher-derivative couplings: Full N=2 superspace does not count!
• The vanishing volume of D=4 superspace
• Stringy KLT relations, global symmetries, and E_7(7) violation
• Nonlinear Self-Duality and Supersymmetry
• Novel supermultiplets of SU(2,2|4) and the AdS_5/CFT_4 duality
• On the U(1) duality anomaly and the S-matrix of N=4 supergravity
• E7(7) symmetry in perturbatively quantised N=8 supergravity
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• E{7(7)} Symmetry and Finiteness of N=8 Supergravity
• Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories
• Counterterms vs. Dualities
• Towards the complete N=2 superfield Born-Infeld action with partially broken N=4 supersymmetry
• Covariant procedures for perturbative non-linear deformation of duality-invariant theories
• N=8 Counterterms and E7(7) Current Conservation
• Construction of all N=4 conformal supergravities
• Superconformal symmetry and maximal supergravity in various dimensions
• The off-shell 4D/5D connection
• Born-Infeld with Higher Derivatives
• Born-Infeld-Goldstone superfield actions for gauge-fixed D-5- and D-3-branes in 6d
• N=8 Supergravity on the Light Cone
• N=2 Supersymmetry and U(1)-Duality
• Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity
• Creation of Matter in the Universe and Groups of Type E7
• New E77 invariants and amplitudes
• Absence of U(1) Anomalous Superamplitudes in $\mathcal{N}\ge 5$ Supergravities
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• The D^{2k} R^4 Invariants of N=8 Supergravity
• Conformal Anomalies and Gravitational Waves
• Cancellation of Conformal and Chiral Anomalies in $N\ge 5$ supergravities
• Duality Constraints on Counterterms in $\mathcal{N}=5,6$ Supergravities
• The Action with Manifest E7 Type Symmetry
• N=2 Supergravity Counterterms, Off and On Shell
• Uniqueness of $\mathcal{N}=2$ and $3$ pure supergravities in 4D
• On quantum compatibility of counterterm deformations and duality symmetries in $\mathcal{N}\ge 5$ supergravities

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