{"product_id":"automorphic-forms-von-oscar-klevang","title":"Automorphic Forms","description":"\u003cp\u003eIn this work we give an introduction to automorphic  forms in string theory by examining a well-known  case in ten-dimensional Type IIB superstring theory.  An automorphic form, constructed as a non-holomorphic  Eisenstein series, is known to encode all  perturbative and non-perturbative quantum  corrections in the genus expansion for the R^4-term  included in the asymptotic string expansion for the  effective action.  Furthermore, we study Type IIA superstring theory  compactified on a rigid Calabi-Yau threefold. Here a  discrete group, the Picard modular group, is  believed to be a preserved symmetry of the quantum  theory, and an automorphic form is conjectured to  encode the quantum corrections to the metric of the  hypermultiplet moduli space, which classically is a  coset space. To read off the loop corrections  arising from the string coupling, as well as the non- perturbative instanton corrections, we rewrite the  Eisenstein series as a Fourier series. The Fourier  series is decomposed into a constant, abelian and  non-abelian part. The main complication arises when  trying to identify the coefficients in the non- abelian part. We try to bring some clarity to this  issue.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783844316902\"\u003e\u003ch3\u003ein String Theory\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783844316902","offer_id":39469960691805,"sku":"9783844316902","price":59.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/483ceda3-1310-481a-9c2b-ac0ba84921c2.jpg?v=1759037249","url":"https:\/\/shop.autorenwelt.de\/en\/products\/automorphic-forms-von-oscar-klevang","provider":"Autorenwelt Shop","version":"1.0","type":"link"}