Prof. Dr. Albrecht Klemm

E-Mail: aklemm(at)
Telefon: +49 228 73 2319
Raum: PI 127
Standort: Physics Institute
Institute: Hausdorff Center for Mathematics - HCM
Forschungsbereich: Research Area C (Leader)

Academic Career


Diploma, University of Mainz


PhD, University of Heidelberg

1990 - 1993

Research Fellow, LMU and TU Munich

1993 - 1994

Research Fellow, Harvard University, Cambridge, MA, USA

1994 - 1996

Research Fellow, CERN TH-Division, Geneva, Switzerland

1996 - 1998

Research Fellow, Enrico Fermi Institute, Chicago, IL, USA


Habilitation, LMU Munich

1998 - 2000

Heisenberg Fellow, Institute for Advanced Study, Princeton, NJ, USA

2000 - 2003

Professor (C3), HU Berlin

2003 - 2006

Associate Professor, University of Madison, WI, USA

2006 - 2007

Professor, University of Madison, WI, USA

Since 2007

Professor (W3), University of Bonn

Research Profile

Super String Theory is a mayor attempt to unify gauge theories with quantum gravity. Compactifications of string theory on varieties with special holonomy including calibrated submanifolds leads to quantum theories in various dimensions. Mathematical well defined sub-sectors of these theories are the topological string- and field theories. Their correlators determine topological invariants of the geometric setting. Often are different physical formulations with different manifest symmetries and duality symmetries among them available. Based on these we extended the methods to calculate the correlators exactly, such as mirror symmetry, the string/gauge theory correspondence, the modular-- and the integrable system approach. In particular using the string/gauge theory correspondence we provided with the topological vertex and the topological recursions two major tools, which are widely in use. We used mirror symmetry and the modular approach to obtain high genus amplitudes on compact Calabi-Yau spaces and showed that the all genus topological string amplitudes on elliptically fibred Calabi-Yau spaces can be expressed in terms of meromorphic Jacobi forms.

Research Projects and Activities

DFG Project KL2271/1-1: “Exakte Methoden in Eich- und String-Theorien”

Bethe Center for Theoretical Physics

DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Principal Investigator

Contribution to Research Areas

Research Area C
A relation between the modular anomaly of topological string theory on elliptic Calabi-Yau spaces and the chiral anomaly of certain six dimensional superconformal theories was discovered recently [1,2,3,4]. As was shown in the eighties, six is the maximal dimension in which these remarkable superconformal symmetries can be realized in quantum theories. The theories are self dual, couple to string degrees of freedom, do not admit a Langrangian description and stayed therefore elusive despite the potential to obtain a classification of lower dimensional theories by dimensional reduction. With the new techniques in topological string theory one can obtain information of their spectrum of BPS states [5]. Another application of the refined topological string that we pursue is the study of non-perturbative effects in quantum systems using resurgence. On the geometrical side our group investigates more generally the effective action of four dimensional field theories obtained by dimensional reduction of maximal supersymmetric theories on special holonomy manifolds or manifolds with G-structures. Currently under investigation is a promising class of manifolds with G2 holonomy obtained using the twisted gluing construction proposed by Kovalev.

Selected Publications

[1] Min-xin Huang, Sheldon Katz, Albrecht Klemm
Topological string on elliptic CY 3-folds and the ring of Jacobi forms
J. High Energy Phys. (10): 125, front matter+78
[2] Babak Haghighat, Albrecht Klemm, Guglielmo Lockhart, Cumrun Vafa
Strings of minimal 6d SCFTs
Fortschr. Phys.
, 63: (5): 294--322
[3] Min-xin Huang, Sheldon Katz, Albrecht Klemm
Elliptically fibered Calabi-Yau manifolds and the ring of Jacobi forms
Nuclear Phys. B , 898: : 681--692
[4] Jie Gu, Min-xin Huang, Amir-Kian Kashani-Poor, Albrecht Klemm
Refined BPS invariants of 6d SCFTs from anomalies and modularity
J. High Energy Phys. (5): 130, front matter+61
[5] Jie Gu, Albrecht Klemm, Marcos Mariño, Jonas Reuter
Exact solutions to quantum spectral curves by topological string theory
J. High Energy Phys. (10): 025, front matter+68
[6] A. Klemm, D. Maulik, R. Pandharipande, E. Scheidegger
Noether-Lefschetz theory and the Yau-Zaslow conjecture
J. Amer. Math. Soc.
23: (4): 1013--1040
[7] Mina Aganagic, Albrecht Klemm, Marcos Mariño, Cumrun Vafa
The topological vertex
Comm. Math. Phys. , 254: (2): 425--478
[8] Vincent Bouchard, Albrecht Klemm, Marcos Mariño, Sara Pasquetti
Topological open strings on orbifolds
Comm. Math. Phys. , 296: (3): 589--623
[9] M.-x. Huang, A. Klemm, S. Quackenbush
Topological string theory on compact Calabi-Yau: modularity and boundary conditions
Homological mirror symmetry
of Lecture Notes in Phys. : 45--102
Publisher: Springer, Berlin
[10] Jie Gu, Hans Jockers, Albrecht Klemm, Masoud Soroush
Knot invariants from topological recursion on augmentation varieties
Comm. Math. Phys. , 336: (2): 987--1051
[11] Kentaro Hori, Sheldon Katz, Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil, Eric Zaslow
Mirror symmetry
With a preface by Vafa
of Clay Mathematics Monographs : xx+929
Publisher: American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA
ISBN: 0-8218-2955-6
[12] S. Katz, A. Klemm, R. Pandharipande
On the motivic stable pairs invariants of K3 surfaces
K3 surfaces and their moduli
With an appendix by R. P. Thomas
of Progr. Math. : 111--146
Publisher: Birkhäuser/Springer, [Cham]
DOI: 10.1007/978-3-319-29959-4_6

Publication List

MathSciNet Publication List (external link)


• Zeitschrift für Naturforschung A


1998 - 2001

Heisenberg Fellow, IAS, Princeton, NJ, USA


Andrejewski Lecturer, Berlin and Potsdam


Simons Professor, Berkeley, CA, USA


Guest Professor, École Normale Supérieure, Paris, France


Frederick W. and Lois B. Gehring Visiting Professor, LSA Mathematics, University of Michigan, Ann Arbor, MI, USA


Visiting Professor, École Normale Supérieure, Paris, France


Visiting Professor, MSRI, Berkeley, CA, USA

Selected Invited Lectures


Minicourse “The Topological Vertex and its Applications”, Instituto Superior Técnico, Lisbon, Portugal


Minicourse “Direct Integration in Topological String Theory”, Workshop on “Geometry and Physics”, Chendgu, China


Minicourse “Topological Strings, Modularity and non-perturbative Physics”, Erwin Schroedinger Institute, Vienna, Austria


Minicourse “Topological Gauge and String theories”, ENS Paris, France


“Direct integration in General Omega Backgrounds”, Banff, AB, Canada


String-Math, Philadelphia, PA, USA


String-Math, Edmonton, AB, Canada


“Topological string on elliptic CY 3-folds and the ring of weak Jacobi forms”, in “Motivic invariants related to K3 and abelian geometries”, Berlin


“Elliptically fibred Calabi-Yau and the ring of weak Jacobi Forms”, in Workshop of “Moduli Spaces in algebraic Geometry and Physics”, Tianjin, China


“F-theory at 20”, California Institute of Technology, CA, USA


“Jacobi Forms and Curve Counting”, at the Workshop “Curves on surfaces and 3-folds”, Centre Interfacultaire Bernoulli CIB Lausanne, Switzerland


“Topological String and Jacobi Forms”, Workshop on “Geometric Correspondence of Gauge Theories”, Trieste, Italy



University of Colorado, Boulder, CO, USA


Ralph Blumenhagen (2002), now Permanent Staff Member, Max Planck Institute for Physics, Munich

Selected PhD students

Babak Haghighat (2009): “On Topological String Theory with Calabi-Yau Backgrounds”,
now Postdoc, Harvard University, MA, USA

Denis Klevers (2011): “Holomorphic Couplings In Non-Perturbative String Compactifications”,
now Fellow, CERN, Theoretical Physics Department, Switzerland

Jie Gu (2014): “Braiding knots with topological Strings”,
now Postdoc, LPTHE ENS Paris, France

Supervised Theses

  • Master theses: 5, currently 2
  • Diplom theses: 4
  • PhD theses: 12, currently 8
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