The emergence of flagpole and flag-dipole fermions in fluid/gravity correspondence

Abstract

The emergence of flagpole and flag-dipole singular spinor fields is explored, in the context of fermionic sectors of fluid/gravity correspondence, arising from the duality between the gravitino, in supergravity, and the phonino, in supersymmetric hydrodynamics. Generalized black branes, whose particular case consists of the AdS-Schwarzschild black brane, are regarded. The correspondence between hydrodynamic transport coefficients, and the universal absorption cross sections of the generalized black branes, is extended to fermionic sectors, including supersound diffusion constants. A free parameter, in the generalized black brane solution, is shown to control the flipping between regular and singular fermionic solutions of the equations of motion for the gravitino. I. INTRODUCTIONClassical spinor fields were classified studying all the possibilities to evaluate their respective bilinear covariants that either satisfy the Fierz identities or their generalizations. This feature has introduced the Lounesto's spinor field classification into six classes of spinor fields, assuming the U(1) gauge symmetry of quantum electrodynamics [1]. A second quantized version of such a classification was introduced in Ref. [2], where quantum spinors and their correlators provided a setup for a second quantized classification. Going further, encompassing SU(2) × U(1) gauge symmetry, a new classification, embracing spinor field multiplets that represent non-Abelian gauge fields, was lately introduced in Ref. [3]. Recently, new classes of fermionic fields on 7manifolds were derived [4,5], regarding, in particular, the AdS 5 × S 5 and AdS 4 × S 7 compactifications [6], also including new fermionic solutions of M-theory compactifications with one supersymmetry [7]. These new classes emulate singular spinor fields on higher dimensions and more general signatures. Hence, it is natural to further explore the role of the spinor fields classifications in the fluid/gravity correspondence setup.The low-energy/low-momentum limit of the AdS/CFT correspondence is also known as fluid/gravity correspondence. In this regime, the field theory side is taken to be an effective theory, hence, hydrodynamics [8]. On the other hand, the compactification of higher dimensions leads the gravitational theory to conventional General Relativity (GR), although this gives some freedom to play with extensions of GR and investigation of its dual theories. This fact has lead to successful predictions of transport coefficients in strongly coupled field theories, being the quark-gluon plasma [9] the most famous example, but not the only one, also appearing in other setups, like the graphene [10], superconductors [11], and Fermi

Deformed AdS$$_4$$–Reissner–Nordström black branes and shear viscosity-to-entropy density ratio

“…[13,14]. Tests of AdS/CFT have been performed in cases for which the supergravity backgrounds are supersymmetric [15,16]. However, a static AdS black hole in the supersymmetric limit can have a naked singularity, avoided when rotation is assumed, as in the Reissner-Nordström spacetime.…”

Gravitational decoupling of generalized Horndeski hybrid stars

“…( 3). This description of fermionic matter can be alternatively implemented in the fluid/gravity correspondence [99]. The resulting system can be thus solved numerically, with boundary conditions, lim…”

Polar form of spinor fields from regular to singular: the flag-dipoles

“…This development is general. Now is time to perform the classification of spinor fields, and for that we will closely follow the Lounesto classification, based on the bi-linear spinor fields [1][2][3][4][5][6][7][8][9][10]. Since all the bi-linear spinors are tensors, such a classification, based on vanishing these tensors, is manifestly generally covariant.…”

“…However, this leaves the door open for an altogether different type of spinors having both scalar and pseudo-scalar bi-linear quantities vanishing identically, called singular [1,2]. Singular spinor fields, or flag-dipole spinor fields, may be unusual but they still have many important things to tell [3][4][5][6][7][8][9][10]. In fact, these spinors can be further split into subclasses, obtained when the axial-vector bi-linear quantity, that is the spin, is zero, and in this case they are called flagpole spinors, or when the antisymmetric tensor bi-linear quantity, that is the momentum, is zero, and in this case they are called dipole spinors.…”