Seminar quantum physics and geometry
**Topological conformal field theory **

Coordination: Christoph Schweigert and Jörg Teschner

21.10.2010: 1. Open/closed TFT

Speaker: Christoph Schweigert, Contact: Christoph Schweigert

References: [L,LP,MS].
Notes

Information: Colloquium talk by
Jacopo Stoppa
(Trinity College, Cambridge)

Place: Geomatikum

4.11.2010: 2. Examples of open/closed TFT
models

Speaker: Jörg Teschner, Contact: Jörg Teschner

References: [HLL]
Notes

Summary:

- Notion of (chain-level) TCFT:

I was following [C1], Section 1.1. The key condition on F is somewhat hidden on the lower half of page 4, there written as F(d\alpha)=df(\alpha). This is what is referred to as condition (B) in my notes. The precursors of this definition by Segal and Getzler are spelled out in Section 3 of Getzler's paper [G] (which can be read independently from the rest). They differ from Costello's definition essentially by replacing the homology of the moduli spaces by its cohomology. A useful-looking survey can also be found in arXiv:0906.5198 by Blumberg, Cohen, Teleman. - Relation to string theory:

I found Dijkgraaf's Les Houches lectures (hep-th/9703136) useful. The functorial definition of Segal/Getzler is recalled in Section 8.7., and Section 8.1. lists basic axioms for an abstract formulation of string theory (page 5 of my notes). - Relation to A_{\infty}-algebras:

The paper [HLL] of Herbst, Lazaroiu, Lerche contains many results and discussions relevant for the open surface generalization (considering elements of Q-cohomology, these authors find what is called minimal A_{\infty} structures, corresponding to m_1=0). A look at section 1. of arXiv:hep-th/0606283 may also be helpful to see the relation between the appearance of A_{\infty}-structures in my lecture and the compactification of moduli spaces of punctured discs. This reference also contains some discussion and further references to the relation with string field theory.

Information: Colloquium talk by Roberto Longo (Rom)

Place: DESY

18.11.2010: 3. A-infinity algebras

Speakers: Sebastian Novak and Christoph Wockel,
Contact: Christoph Schweigert

References: [PS]

Information: Colloquium talk by NN

Place: Geomatikum

For information:

29.11-3.12.2010:
From Sigma Models to Four-dimensional QFT

Workshop at DESY

16.12.2010: ZMP seminar and only the seminar
cancelled because of dies academicus

Information: Colloquium talk by
Karl-Hermann Neeb
(Erlangen)

Place: Geomatikum

13.1.2011: 4. Costello's construction of TCTs

Speaker: Vito Iacovino

References: [C2]

Information: Colloquium talk by
Fabian
Essler (Oxford):
``Finite Temperature and Quantum Quench Dynamics in Massive
Integrable Quantum Field Theories''

Place: DESY

27.1.2011: 5. On the relation between open and closed
topological strings

Speaker: Tom Brown

References: [HLL, C1].
Notes of the speaker.

Information: Colloquium talk by Andreas
Ludwig (UCSB)

Place: Geomatikum H2

Literatur

- [C1] Kevin J. Costello: Topological conformal field theories and Calabi-Yau categories arXiv:math/0412149v7 [math.QA]
- [C2] Kevin J. Costello: A dual point of view on the ribbon graph decomposition of moduli space arXiv:math/0601130v1 [math.GT]
- [G] Ezra Getzler: Batalin-Vilkovisky algebras and two-dimensional topological field theories arXiv:hep-th/9212043v3
- [HLL] Manfred Herbst, C.I. Lazaroiu, Wolfgang Lerche: Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings arXiv:hep-th/0402110v2
- [KR] A. Kapustin, L. Rozansky: On the relation between open and closed topological strings arXiv:hep-th/0405232v2
- [L] C. I. Lazaroiu: On the structure of open-closed topological field theory in two dimensions arXiv:hep-th/0010269v2
- [LP] Aaron D. Lauda, Hendryk Pfeiffer: Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras arXiv:math/0510664v3 [math.AT]
- [MS] Gregory W. Moore, Graeme Segal: D-branes and K-theory in 2D topological field theory arXiv:hep-th/0609042v1
- [PS] Michael Penkava, Albert Schwarz:
A_\infty Algebras and the Cohomology of Moduli Spaces
arXiv:hep-th/9408064v2

Seminar quantum physics and geometry ,*email:*schweigert@math.uni-hamburg.de