Hidden relations of central charges and OPEs in holographic CFT

It is known that the (a, c) central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants. We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition. We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition. Furthermore, we prove that the consequential relation c = 1/3ℓeff∂a/∂ℓeff and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.

Logarithmic corrections to the entropy of non-extremal black holes in $$ \mathcal{N} $$ = 1 Einstein-Maxwell supergravity

We reviewed the field redefinition approach of Seeley-DeWitt expansion for the determination of Seeley-DeWitt coefficients from arXiv:1505.01156. We apply this approach to compute the first three Seeley-DeWitt coefficients for “non-minimal” $$ \mathcal{N} $$ N = 1 Einstein-Maxwell supergravity in four dimensions. Finally, we use the third coefficient for the computation of the logarithmic corrections to the Bekenstein-Hawking entropy of non-extremal black holes following arXiv:1205.0971. We determine the logarithmic corrections for non-extremal Kerr-Newman, Kerr, Reissner-Nordström and Schwarzschild black holes in “non-minimal” $$ \mathcal{N} $$ N = 1, d = 4 Einstein-Maxwell supergravity.

Revisit of renormalization of Einstein-Maxwell theory at one-loop

In a series of the recent works based on foliation-based quantization in which renormalizability has been achieved for the physical sector of the theory, we have shown that the use of the standard graviton propagator interferes, due to the presence of the trace mode, with the 4D covariance. A subtlety in the background field method also requires careful handling. This status of the matter motivated us to revisit an Einstein-scalar system in one of the sequels. Continuing the endeavors, we revisit the one-loop renormalization of an Einstein-Maxwell system in the present work. The systematic renormalization of the cosmological and Newton’s constants is carried out by applying the refined background field method. One-loop beta function of the vector coupling constant is explicitly computed and compared with the literature. The longstanding problem of gauge choice-dependence of the effective action is addressed and the manner in which the gauge-choice independence is restored in the present framework is discussed. The formalism also sheds light on background independent analysis. The renormalization involves a metric field redefinition originally introduced by ‘t Hooft; with the field redefinition the theory should be predictive.

Four-dimensional vector multiplets in arbitrary signature (II)

Following the classification up to isomorphism of [Formula: see text] Poincaré Lie superalgebras in four dimensions with arbitrary signature obtained in a companion paper, we present off-shell vector multiplet representations and invariant Lagrangians realizing these algebras. By dimensional reduction of five-dimensional off-shell vector multiplets, we obtain two representations in each four-dimensional signature. In Euclidean and neutral signature, these representations can be mapped to each other by a field redefinition induced by the action of the Schur group on the space of superbrackets. In Minkowski signature, we show that the superbrackets underlying the two vector multiplet representations belong to distinct open orbits of the Schur group and are therefore inequivalent. Our formalism allows to answer questions about the possible relative signs between terms in the Lagrangian systematically by relating them to the underlying space of superbrackets.

A pure spinor twistor description of the D = 10 superparticle

We present a novel twistor formulation of the ten-dimensional massless super-particle. This formulation is based on the introduction of pure spinor variables through a field redefinition of another model for the superparticle, and in the new description we find that the super-Pauli-Lubanski three-form naturally arises as a constraint. Quantization is studied in detail for both models and they are shown to correctly describe the D = 10 super-Yang-Mills states.

Inflation in Supergravity from Field Redefinitions

Supergravity (SUGRA) theories are specified by a few functions, most notably the real Kähler function denoted by G ( T i , T ¯ i ) = K + log | W | 2 , where K is a real Kähler potential, and W is a holomorphic superpotential. A field redefinition T i → f 1 ( T i ) changes neither the theory nor the Kähler geometry. Similarly, the Kähler transformation, K → K + f 2 + f ¯ 2 , W → e − f 2 W where f 2 is holomorphic and leaves G and hence the theory and the geometry invariant. However, if we perform a field redefinition only in K ( T i , T ¯ i ) → K ( f ( T i ) , f ( T ¯ i ) ) , while keeping the same superpotential W ( T i ) , we get a different theory, as G is not invariant under such a transformation while maintaining the same Kähler geometry. This freedom of choosing f ( T i ) allows construction of an infinite number of new theories given a fixed Kähler geometry and a predetermined superpotential W. Our construction generalizes previous ones that were limited by the holomorphic property of W. In particular, it allows for novel inflationary SUGRA models and particle phenomenology model building, where the different models correspond to different choices of field redefinitions. We demonstrate this possibility by constructing several prototypes of inflationary models (hilltop, Starobinsky-like, plateau, log-squared and bell-curve) all in flat Kähler geometry and an originally renormalizable superpotential W. The models are in accord with current observations and predict r ∈ [ 10 − 6 , 0.06 ] spanning several decades that can be easily obtained. In the bell-curve model, there also exists a built-in gravitational reheating mechanism with T R ∼ O ( 10 7 G e V ) .

On Goldstone Fields with Spin Higher than 1/2

We review the properties of 3d non-linear models of vector and vector-spinor Goldstone fields associated with the spontaneous breaking of certain higher-spin counterparts of supersymmetry (so-called Hietarinta algebras), whose Lagrangians are of the Volkov–Akulov type. At the quadratic order, these Lagrangians contain, respectively, the Chern–Simons and Rarita–Schwinger terms. The vector Goldstone model has a propagating degree of freedom which, in a decoupling limit, is a quartic Galileon scalar field (similar to those appearing in models of modified gravity). On the other hand, the vector-spinor goldstino retains the gauge symmetry of the Rarita–Schwinger action and eventually reduces to the latter by a non-linear field redefinition. We thus find that, in three space-time dimensions, the free Rarita–Schwinger action is invariant under a hidden rigid symmetry generated by fermionic vector-spinor operators and acting non-linearly on the Rarita–Schwinger goldstino.

Are there really conformal frames? Uniqueness of affine inflation

Here, we concisely review the nonminimal coupling dynamics of a single scalar field in the context of purely affine gravity and extend the study to multifield dynamics. The coupling is performed via an affine connection and its associated curvature without referring to any metric tensor. The latter arises a posteriori and it may gain an emergent character like the scale of gravity. What is remarkable in affine gravity is the transition from nonminimal to minimal couplings which is realized by only field redefinition of the scalar fields. Consequently, the inflationary models gain a unique description in this context where the observed parameters, like the scalar tilt and the tensor-to-scalar ratio, are invariant under field reparametrization. Overall, gravity in its affine approach is expected to reveal interesting and rich phenomenology in cosmology and astroparticle physics.

Renormalization of Einstein gravity through a derivative-dependent field redefinition

This work explores an alternative solution to the problem of renormalizability in Einstein gravity. In the proposed approach, Einstein gravity is transformed into the renormalizable theory of four-derivative gravity by applying a local field redefinition containing an infinite number of higher derivatives. It is also shown that the current–current amplitude is invariant with the field redefinition, and thus the unitarity of Einstein gravity is preserved.