Towards understanding the ultraviolet behavior of quantum loops in infinite-derivative theories of gravity

Abstract

In this paper we will consider quantum aspects of a non-local, infinitederivative scalar field theory -a toy model depiction of a covariant infinitederivative, non-local extension of Einstein's general relativity which has previously been shown to be free from ghosts around the Minkowski background. The graviton propagator in this theory gets an exponential suppression making it asymptotically free, thus providing strong prospects of resolving various classical and quantum divergences. In particular, we will find that at 1-loop, the 2-point function is still divergent, but once this amplitude is renormalized by adding appropriate counter terms, the ultraviolet (UV) behavior of all other 1-loop diagrams as well as the 2-loop, 2-point function remains well under control. We will go on to discuss how one may be able to generalize our computations and arguments to arbitrary loops.

Quantum radiation from a sandwich black hole

“…Theories of quantum gravity, such as the string theory and the loop gravity, are well known examples. Recently a new, very promising UV-complete modifications of the general relativity was proposed [1][2][3][4][5][6][7][8][9][10]. It is called a ghost-free gravity.…”

Wald Entropy for Ghost-Free, Infinite Derivative Theories of Gravity

“…However, the form of F 's do tell us of some interesting aspects of gravity in the UV -namely, the gravitational interaction becomes non-local [10,11] and helps us to understand the quantum behaviour of gravity at higher loops, i.e. above 1-loop there are indications that the theory is convergent [17][18][19][20]; explicit computations have been performed in a toy model up to 2-loops [20]. Further note that S UV W = 0 will have a very interesting consequence for the the third law of thermodynamics in the context of gravity, which might hint towards the absolute ground state of gravity, when the condition, Eq.…”

“…(15), the vertex factor for any graviton-graviton interaction will also be enhanced by a factor a(k 2 ). One such study has been performed in the context of singularity free gravity [20], where the form of a(k 2 ) ∼ e k 2 /M 2 has been suggested, motivated by string field theory, where the vertex operator get similarly exponentially enhanced. In this particular case, it has been shown that the blackhole singularity for a spherically symmetric metric disappears in the linearised limit, therefore ameliorating the UV nature of gravity [10] 1 .…”

Nonlocal N = 1 $$ \mathcal{N}=1 $$ supersymmetry

“…In particular a nonlocal extension of the Einstein gravity has a variety of interesting properties and applications (see, e.g., [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]). It is also known that nonlocal theories capture certain aspects of string theory, particularly in the context of string field theory and p-adic string (see, e.g., [31][32][33][34][35][36][37][38][39][40][41]).…”