New matter multiplets in N=2 conformal supergravity

Knowledge of multiplets in conformal supergravity plays an important role in constructing supergravity theories in the superconformal framework. In N= 2 conformal supergravity, a 24+24 (bosonic + fermionic) components "real scalar multiplet" was found in the paper "24 + 24 real scalar multiplet in four dimensional N = 2 conformal supergravity" It was also found that one could impose a consistent set of constraints to reduce this multiplet into an $8+8$ component tensor multiplet. The set of constraints implicitly used a multiplet containing the phase of a complex scalar. However, this multiplet was not explicitly constructed in the paper. Our goal is towards an explicit construction of this new multiplet.

We attempt at an explicit construction of this multiplet solving the multiplet. We are looking at the constraints that are imposed on the combination of the real scalar multiplet and this multiplet and see what kind of multiplets the constraints themselves form. This is similar to what was known in the case of N=2 chiral multiplet in the paper "Structure of N = 2 supergravity" by B.De Wit et. at. The N=2 chiral multiplet is a 16+16 component multiplet. However, it was found that for a specific choice of chiral and Weyl weight, one can impose an 8+8 set of constraints on the chiral multiplet to reduce it to an 8+8 component restricted chiral multiplet. The set of 8+8 constraints themselves constituted the tensor multiplet. Our present analysis will equip us with two new multiplets. We would like to see how these new multiplets fit into the superconformal formalism for the construction of N=2 supergravity theories and how they affect the higher derivative structure of the theory. Subsequently, we would like to see the effect of the new higher derivative structure on the computation of black hole entropy.

Superconformal construction of N=2 supergravity

Why do we study conformal supergravity?

The efforts to construct a unified fundamental theory describing all the forces in nature has led to the formulation of two remarkable, mutually exclusive theories - General relativity (GR) and the Standard Model (SM). General relativity explains gravity as the geometry of space-time and describes the macroscopic world. However, in the microscopic world, gravity is negligible due to the dominance of other interactions. The microscopic regime is thus explained by the Standard Model, which is constructed in the framework of Quantum field theory (QFT). QFT considers fields as fundamental objects, and particles are represented as quantum fluctuations of these fields. However, these theories have issues that have to be fixed. Physicists are not completely satisfied with the SM as it has many issues , including the hierarchy problem. Thus one cannot rule out the possibility of a unified theory in which GR and SM could be special cases.

At the Planck scale of energy, gravitational interaction becomes comparable to the strength of other interactions. Thus, at this energy scale, we need a quantum theory that incorporates gravity and other interactions. However, the gravitational coupling constant has a fixed mass dimension. As a result, power counting arguments imply that the amplitude is divergent. Hence general relativity is non-renormalizable. The search to find a renormalizable theory that unifies SM and GR led to the discovery of superstring theory. Superstring theory is a possible theory of quantum gravity that can be defined in 10 dimensions, with 9 spatial and 1 time dimensions, in which the fundamental objects are one-dimensional strings. Firstly it incorporates gravity, as the spectrum of the string contains a massless spin 2 particle together with many massless spin 1 particles. Secondly, as the fundamental objects are one-dimensional strings, it removes the divergences that arise from considering point-like objects as fundamental particles. Thus string theory is UV finite. Supersymmetry becomes a required feature of string theory in order to remove some of the undesirable aspects of the bosonic string theory. Supersymmetry (SUSY) is a space-time symmetry that relates bosons to fermions. SUSY introduces more fermions in its spectrum, making it more physical and also removes unphysical tachyonic modes in the bosonic strings.

Though string theory is a consistent theory of quantum gravity, there are no experimental evidences yet. This is due to the immense difficulty in achieving the Planck scale of energy. Even the most advanced accelerators are far away from achieving this energy scale. However, there is a possibility that string theory could be tested indirectly in the future if we study the low energy limit of superstring theory. Thus it is crucial to understand the concepts of supergravity.

Supergravity is the low energy limit of the superstring theory. It can also be realized as a gauge theory of local supersymmetry which we will discuss in this thesis. There are many motivations to construct a theory of supergravity. Supergravity unifies other gauge interactions with gravity. It predicts the fermionic superpartner of graviton - the gravitino, which has a spin 3/2. It also provides a possible candidate for dark matter - the neutralino. Conformal supergravity plays an important role in the off-shell formulation of supergravity theories, which on the other hand, plays an important role in the computation of black hole entropy, including the higher derivative corrections and match them with the microscopic results. Superconformal multiplets play a crucial role in the superconformal framework, and it is important to study them in detail.

Modified Symmetric teleparallel gravity in higher dimensions

In this work, a more general version of modified symmetric teleparallel gravity f(Q) gravity in six dimensions is conceptualized. Here the non-zero non-metricity tensor is the fundamental object, which is torsion-less and curvature-less. The most general field equations are found for a generic Lagrangian f(Q)+L, where f(Q) is a function of a quadratic scalar Q built from irreducible components of the nonmetricity tensor, and L is the matter Lagrangian. The interior and the exterior of the six-dimension axi-symmetric warped brane for a power-law model of f(Q) is studied. It is found that, in the absence of a bulk cosmological constant, the non-metricity of the spacetime yields to a warped compactified spacetime. Moreover, the non-metrcity induces a transition from six-dimensional AdS to dS spacetime in the exterior of the brane. The manuscript of this work is under preparation.