arXiv subjects

Katrin Wendland

Publications and source records attributed to Katrin Wendland.

23 records · Page 2Linked to original sources

arXiv2003

Mirror Symmetry on Kummer Type K3 Surfaces

We investigate both geometric and conformal field theoretic aspects of mirror symmetry on N=(4,4) superconformal field theories with central charge c=6. Our approach enables us to determine the action of mirror symmetry on (non-stable) singular fibers in elliptic fibrations of Z_N orbifold limits of K3. The resulting map gives an automorphism of order 4,8, or 12, respectively, on the smooth universal cover of the moduli space. We explicitly derive the geometric counterparts of the twist fields in our orbifold conformal field theories. The classical McKay correspondence allows for a natural interpretation of our results.

hep-th↗

arXiv2002

Orbifold Constructions of K3: A Link between Conformal Field Theory and Geometry

We discuss geometric aspects of orbifold conformal field theories in the moduli space of N=(4,4) superconformal field theories with central charge c=6. Part of this note consists of a summary of our earlier results on the location of these theories within the moduli space [NW01,Wen] and the action of a specific version of mirror symmetry on them [NW]. We argue that these results allow for a direct translation from geometric to conformal field theoretic data. Additionally, this work contains a detailed discussion of an example which allows the application of various versions of mirror symmetry on K3. We show that all of them agree in that point of the moduli space.

hep-th↗

arXiv2002

Consistency of Orbifold Conformal Field Theories on K3

We explicitly determine the locations of G orbifold conformal field theories, G=Z_M, M=2,3,4,6, G=\hat D_n, n=4,5, or G the binary tetrahedral group \hat T, within the moduli space M^{K3} of N=(4,4) superconformal field theories associated to K3. This is achieved purely from the known description of the moduli space [AM94] and the requirement of a consistent embedding of orbifold conformal field theories within M^{K3}. We calculate the Kummer type lattices for all these orbifold limits. Our method allows an elementary derivation of the B-field values in direction of the exceptional divisors that arise from the orbifold procedure [Asp95,Dou97,BI97], without recourse to D-geometry. We show that our consistency requirement fixes these values uniquely and determine them explicitly. The relation of our results to the classical McKay correspondence is discussed.

hep-th↗

arXiv2000

Crystallographic Orbifolds: Towards a Classification of Unitary Conformal Field Theories with Central Charge c = 2

We study the moduli space C^2 of unitary two-dimensional conformal field theories with central charge c=2. We construct all the 28 nonexceptional nonisolated irreducible components of C^2 that may be obtained by an orbifold procedure from toroidal theories. The parameter spaces and partition functions are calculated explicitly, and all multicritical points and lines are determined. We show that all but four of the 28 irreducible components of C^2 corresponding to nonexceptional orbifolds are directly or indirectly connected to the moduli space of toroidal theories in C^2. We relate our results to those by Dixon, Ginsparg, Harvey on the classification of c=3/2 superconformal field theories and thereby give geometric interpretations to all nonisolated orbifolds discussed there.

hep-th↗

arXiv1999

Extremal Kaehler metrics and Ray-Singer analytic torsion

Let (X,[ω]) be a compact Kaehler manifold with a fixed Kaehler class [ω]. Let K_ωbe the set of all Kaehler metrics on X whose Kaehler class equals [ω]. In this paper we investigate the critical points of the functional Q(g)= |v|_g T_0(X,g)^{1/2} for g \in K_ω, where v is a fixed nonzero vector of the determinant line λ(X) associated to H^*(X) and T_0(X,g) is the Ray-Singer analytic torsion. For a polarized algebraic manifold (X,L) we consider a twisted version Q_L(g) of this functional and assume that c_1(L)=[ω]. Then the critical points of Q_L are exactly the metrics g\in K_ωof constant scalar curvature. In particular, if c_1(X)=0 or if c_1(X)<0 and 1/(2π)[ω] = -c_1(X), then K_ωcontains a unique Kaehler-Einstein metric g_{KE} and Q_L attains its absolut maximum at g_{KE}.

math.DG↗