Constraints on the action of effective theories in quantum gravity
Oct 21, 2024287 pages
Thesis: PhD - Centre de Physique Théorique, France
- Published: Oct 21, 2024
Report number:
- tel-04928952,
- 2024IPPAX089
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0 Citations
Abstract: (TEL)
String theory constitutes one of the most popular and studied framework to approach quantum gravity. It is well known that the low energy limit of string theory gives a wide range of effective field theories. One recent and promising way to extract information about quantum gravity from this string landscape has been the swampland program. The string lamppost principle postulates that the quantum gravity landscape and the string landscape coincide. In this thesis we propose to study this claim for the case of higher order Wilson couplings in the very restricted case of maximal supersymmetry.We first study the low energy limit of genus 0, 1 and 2 string amplitudes for type II string theory compactified on a torus and compare them to tree level, 1-loop and 2-loop maximal supergravity amplitudes respectively. This allows us to compute the perturbative contributions to the leading Wilson coefficients of maximally supersymmetric string theory. We also show that in dimension 8 logarithmic divergences of the supergravity amplitudes can be linked to divergences of Wilson couplings. We give a prescription to properly regularise the divergence by using the finite string amplitude.We then use the differential equations entailed by the supersymmetric Ward identities as well as the constraints imposed by U-duality to derive the full non perturbative Wilson coefficients for maximally supersymmetric string theory in dimensions higher or equal to 6. These are given for the leading and next to leading Wilson coefficients by Eisenstein and Epstein series for the relevant U-duality group. The parabolic Fourier expansions of these series can then be used to check the different degeneration limits of the Wilson coefficients.Finally we study the minima of these functions on moduli space to give lower bounds on Wilson coefficients coming from maximally supersymmetric string theory. This implies finding the minima of Epstein series for special values of the s parameter. We first extend Grenier's recursive construction of a fundamental domain to almost any simple Lie group which allows us to properly define the domain of study of our functions. We then show that symmetric points are necessarily extrema of automorphic forms and give precise criteria for them to be minima. We also identify these symmetric points as corners of fundamental domains. We study relevant symmetric points for the case of SL(n) and SO(n,n) groups and give additional density arguments regarding the global minima for large s parameter. We then checked our conjecture numerically for the cases n=5 relevant for dimensions 7 and 6.These lower bounds should then be compared to lower bounds coming from unitarity constraints using S-matrix bootstrap methods. As far as we know this analysis still needs to be performed in dimensions lower or equal to 8. We have shown that in dimension 6 factorisation properties of maximally supersymmetric amplitudes imply that the unitarity properties of superamplitudes reduce to the unitarity properties of scalar amplitudes. These kind of factorisations also exist in other dimensions but do not always lead to such drastic simplifications. However one can always restrict to elastic scattering to make the numerics bearable. This kind of analysis, if successful, would be a strong argument for the validity of the string lamppost principle in the case of maximal supersymmetry.- Quantum gravity
- String theory
- Supergravity
- Gravité quantique
- Théorie des cordes
- Supergravité
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