# Browsing by Author "Schimmrigk, Rolf"

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Item Complex Multiplication Symmetry of Black Hole Attractors(Elsevier, 2003) Lynker, Monika; Periwal, Vipul; Schimmrigk, RolfWe show how Moore’s observation, in the context of toroidal compactifications in type IIB string theory, concerning the complex multiplication structure of black hole attractor varieties, can be generalized to Calabi-Yau compactifications with finite fundamental groups. This generalization leads to an alternative general framework in terms of motives associated to a Calabi-Yau variety in which it is possible to address the arithmetic nature of the attractor varieties in a universal way via Deligne’s period conjecture.Item Emergent Spacetime from Modular Motives(Springer, 2008-12) Schimmrigk, RolfThe program of constructing spacetime geometry from string theoretic modular forms is extended to Calabi-Yau varieties of dimensions two, three, and four, as well as higher rank motives. Modular forms on the worldsheet can be constructed from the geometry of spacetime by computing the L-functions associated to omega motives of Calabi-Yau varieties, generated by their holomorphic n−forms via Galois representations. The modular forms that emerge from the Ω−motive and other motives of the intermediate cohomology are related to characters of the underlying rational conformal field theory. The converse problem of constructing space from string theory proceeds in the class of diagonal theories by determining the motives associated to modular forms in the category of pure motives with complex multiplication. The emerging picture indicates that the L-function can be interpreted as a map from the geometric category of motives to the category of conformal field theories on the worldsheet.Item A General Framework of Automorphic Inflation(Springer Verlag [Commercial Publisher], 2016-05-24) Schimmrigk, RolfAutomorphic inflation is an application of the framework of automorphic scalar field theory, based on the theory of automorphic forms and representations. In this paper the general framework of automorphic and modular inflation is described in some detail, with emphasis on the resulting stratification of the space of scalar field theories in terms of the group theoretic data associated to the shift symmetry, as well as the automorphic data that specifies the potential. The class of theories based on Eisenstein series provides a natural generalization of the model of j-inflation considered previously.Item General Framework of Automorphic Inflation(Springer Verlag, 2016) Schimmrigk, RolfAutomorphic inflation is an application of the framework of automorphic scalar field theory, based on the theory of automorphic forms and representations. In this paper the general framework of automorphic and modular inflation is described in some detail, with emphasis on the resulting stratification of the space of scalar field theories in terms of the group theoretic data associated to the shift symmetry, as well as the automorphic data that specifies the potential. The class of theories based on Eisenstein series provides a natural generalization of the model of j-inflation considered previously. Keywords: Cosmology of Theories beyond the SM, Differential and Algebraic Geometry, Discrete SymmetriesItem Landau–Ginzburg Vacua of String, M- and F-Theory at c = 12(Elsevier [Commercial Publisher], 1998-12) Lynker, Monika; Schimmrigk, Rolf; Wisskirchen, AndreasTheories in more than ten dimensions play an important role in understanding nonperturbative aspects of string theory. Consistent compactifications of such theories can be constructed via Calabi-Yau fourfolds. These models can be analyzed particularly efficiently in the Landau-Ginzburg phase of the linear σ-model, when available. In the present paper we focus on those σ-models which have both a Landau-Ginzburg phase and a geometric phase described by hypersurfaces in weighted projective five-space. We describe some of the pertinent properties of these models, such as the cohomology, the connectivity of the resulting moduli space, and mirror symmetry among the 1,100,055 configurations which we have constructed.Item The Langlands Program and String Modular K3 Surfaces(Nuclear Physics B, 2006-03) Schimmrigk, RolfA number theoretic approach to string compactification is developed for Calabi-Yau hypersurfaces in arbitrary dimensions. The motivic strategy involved is illustrated by showing that the Hecke eigenforms derived from Galois group orbits of the holomorphic two-form of a particular type of K3 surfaces can be expressed in terms of modular forms constructed from the worldsheet theory. The process of deriving string physics from spacetime geometry can be reversed, allowing the construction of K3 surface geometry from the string characters of the partition function. A general argument for K3 modularity follows from mirror symmetry, in combination with the proof of the Shimura-Taniyama conjecture.Item A modularity test for elliptic mirror symmetry(Physics Letters B, 2007) Schimmrigk, RolfIn this Letter a previously initiated program to construct space from modular forms on the string worldsheet is applied to mirror symmetry. Predictions of an algebraic mirror construction are confirmed for elliptic curves of Brieskorn–Pham type by showing that the string theoretic modular forms associated to the Hasse–Weil L-series of mirror pairs of such curves are identical.Item Multiﬁeld Reheating after Modular j-Inﬂation(Elsevier, 2018-03-22) Schimmrigk, RolfIn the inﬂationary framework of cosmology the initial phase of rapid expansion has to be followed by a reheating stage, which is envisioned to end in a radiation dominated big bang. Key parameters that characterize this big bang state are the temperature at the end of the reheating stage and the baryon asymmetry. For general interacting theories these parameters are diﬃcult to obtain analytically because of the involved structure of the potential. In this paper multiﬁeld reheating is considered for interacting theories in which the inﬂaton trajectory is weakly curved. This scenario is realized in the model of j-inﬂation, a particular example of modular inﬂation, allowing an estimate of the reheat temperature.Item On Flux Vacua and Modularity(Springer, 2020-09) Schimmrigk, RolfGeometric modularity has recently been conjectured to be a characteristic feature for ﬂux vacua with W = 0. This paper provides support for the conjecture by computing motivic modular forms in a direct way for several string compactiﬁcations for which such vacua are known to exist. The analysis of some Calabi-Yau mani-folds which do not admit supersymmetric ﬂux vacua shows that the reverse of the conjecture does not hold.