Higher-form symmetries in supergravity, scalar charges and black-hole thermodynamics

A

bstract

Minimal 5-dimensional supergravity compactified on a circle gives the T ³ model of

= 2, d = 4 supergravity, whose duality group is SL(2, ℝ ). We study exhaustively the relations between all the local and global symmetries of both theories and between the corresponding conserved currents and charges, including the on-shell closed generalized Komar charges associated to isometries. We find that the 2-dimensional subgroup of SL(2, ℝ ) that does not include electric-magnetic transformations is realized as a higher-form symmetry group that acts on the 5-dimensional metric and vector field. Using the generalized Komar charges we compute the Smarr formulas for black holes, showing that they are identical once the relations between all the 5- and 4-dimensional thermodynamical quantities are taken into account, which is only possible if certain constraints on the fields are satisfied. We notice that on-shell closed 5-dimensional 3-form charges give, upon dimensional reduction, on-shell closed 3-form currents and 2-form charges. The dimensional reduction of the 5-dimensional generalized Komar 3-form charge associated to a Killing vector gives a new 4-dimensional on-shell closed 3-form current which must be associated to a new global symmetry of the theory when it admits that Killing vector. Some of the results that we have derived are valid for theories of Einstein-Maxwell-like theories of ( p + 1)-forms with Chern-Simons terms, which includes 11-dimensional supergravity as a particular example.