# Talks

The following is a list of selected talks I have recently given. This is not a complete collection of all my talks due to two reasons: Firstly, talks which were presented with handwritten slides or on the blackboard are omitted. Secondly, heavy overlap by talks on the same topic is avoided by presenting only the most complete or — in my own opinion — best talk on the subject.

Further below, a selection of talks can be found, which were given by my students on the results of joint research projects, and which I either co-authored or were written under my supervision.

## SLIDES OF SELECTED RECENT TALKS

• Einblick in die Logarithmische Konforme Feldtheorie

### Authors:

Michael Flohr

### Event :

Talk (in german) given on 02. July 2009 at the Department of Physics, University of Bielefeld, Germany.

### Sources and Abstract:

Wir geben eine kurze Einführung in die logarithmische konforme Feldtheorie (LCFT). Die charakterisierende Eigenschaft von LCFT ist das Auftreten von unzerlegbaren Darstellungen der chiralen Symmetrie Algebra.     Wir betonen, dass LCFT eine recht allgemeine Form von konformer Feldtheorie darstellt, die viele Anwendungen besitzt. Sie ist keinesfalls nur eine (kleine) Menge von pathologischen Fällen. Wir geben einen Überblick dazu, wie die meisten der leistungsfähigen Strukturen rationalen konformen Feldtheorie auf den logarithmischen Fall verallgemeinert werden können. In der Tat kann gezeigt werden, dass bestimmte LCFTen im mathematisch strengen Sinne rationale Theorien sind.     Wir präsentieren zwei neuere Resultate: Zuerst stellen wir fermionischen Summen-Darstellungen der Charaktere bestimmter LCFTen vor und zeigen damit, dass diese Theorien in natürlicher Weise in das Klassifikationsschema rationaler konformer Feldtheorien mittels deren Eigenschaften unter der Modulgruppe passen. Abschließend legt die Konstruktion der augmentierten minimalen Modelle nahe, dass jede rationale konforme Feldtheorie zu einer rationalen LCFT erweitert werden kann.

• Glimpses of Logarithmic Conformal Field Theory

### Authors:

Michael Flohr

### Event:

Talk given on 26. June 2008 in the Strings & Fields Semimar at the Arnold Sommerfeld Center for Theoretical Physics, Ludwig Maximilian University Munich, Germany.

### Sources and Abstract:

We give a brief survey on logarithmic conformal field theory (LCFT). The characterizing feature of LCFT is the occurrence of indecomposable representations of the chiral symmetry algebra.
We point out that LCFT is a rather general kind of conformal field theory with many applications, and not just a set of a few pathological cases. We then review how most of the powerful structures of rational conformal field theory can be generalized to the logarithmic case. In fact, it can be proven that certain LCFTs are rational in the mathematically strong sense.
We present two further recent results: Firstly, fermionic sum representations of the characters of certain LCFTs show that these theories naturally fit into the classification scheme of rational CFTs via their modular properties. Secondly, the construction of augmented minimal models suggests that any rational CFT may be extended to a (rational) LCFT.

• Logarithmic Conformal Field Theory

### Authors

Michael Flohr

### Event

Presentation given on 22. May 2008 at the National University of Ireland at Maynooth, Maynooth, Ireland.

### Sources and Abstract

We give a very brief survey on logarithmic conformal field theory (LCFT) and its applications. We explain, what LCFT has in common with ordinary conformal field theory, and where the differences lie.

• $$\boldsymbol{D}$$-Branes in a Non-Compact WZNW Model

### Authors:

Hendrik Adorf and Michael Flohr (Speaker)

### Event  :

Talk given on the Second German-Japanese Workshop on Strings, Non-Commutativity, and All That, January 2008, Hannover, Germany.

### Sources and Abstract

For $$AdS$$ boundary conditions, we give a solution of the $$H_3^+$$ two point function involving degenerate field with $$\mathrm{SL}(2)$$-label $$b^{-2}/2$$, which is defined on the full $$(u,z)$$ unit square. It consists of two patches, one for $$z < u$$ and one for $$u < z$$. Along the $$u = z$$ “singularity”, the solutions from both patches are shown to have finite limits and are merged continuously as suggested by the work of Hosomichi and Ribault. From this two point function, we can derive $$b^{-2}/2$$-shift equations for $$AdS_2$$ D-branes. We show that discrete as well as continuous $$AdS_2$$ branes are consistent with our novel shift equations without any new restrictions.

• Four-Point Functions in Logarithmic Conformal Field Theory

### Authors

Michael Flohr (Speaker) and Marco Krohn

### Event

Talk given at the third annual meeting of the EU-network EUCLID (EUropean Collaboration Linking Integrability with other Disciplines) Integrable Models and Applications: from Strings to Condensed Matter, September 2005 in Santiago de Compostela, Spain.

### Sources and Abstract

An algorithm is presented which computes the generic form of four-point functions of fields residing in indecomposable Jordan cells of arbitrary rank, as they typically appear in logarithmic conformal field theory. There are important differences with respect to the already known case of two- and three-point functions. We discuss some examples and point out recent developements and open problems, in particular concerning theories with vanishing central charge, which may describe disorder phenomena.

• Konforme Feldtheorie und Riemannsche Flächen

### Authors:

Michael Flohr

### Event  :

Talk (in german) given on 2. December 2004 at the Department of Mathematics, University of Münster, Germany.

### Sources:

Ausgehend von einer elementaren Einführung in konforme Feldtheorie mit Hilfe von Vertex-operator-Algebren wird die enge Beziehung zu Riemannschen Flächen motiviert. Dies vermag jedoch nicht alle Aspekte von konformer Feldtheorie zu erfassen. Besonders die sogenannten logarithmischen konformen Feldtheorien stellen hier eine Herausforderung dar. Der Vortrag diskutiert, was logarithmische konforme Feldtheorien sind, wie sie mit der Geometrie Riemannscher Flächen zusammenhängen, und in wie fern sie als rationale konforme Feldtheorien verstanden werden können.

• Four-Point Functions in LCFT - Crossing Symmetry and $$\boldsymbol{\mathrm{SL}(2,\mathbb{C})}$$ Covariance

### Authors:

Michael Flohr (Speaker) and Marco Krohn

### Event  :

Talk given at the 37. International Symposium Ahrenshoop on the Theory of Elementary Particles Recent Developments in String/M-Theory and Field Theory, August 2004 at Akademie Berlin-Schmöckwitz, Germany.

### Sources and Abstract

The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The presented algorithm is illustrated with some non-trivial examples and permutation symmetries are exploited to reduce the number of free structure-functions, which cannot be fixed by global conformal invariance alone.

• Logarithmic Conformal Field Theory in a (Nut)Shell

### Authors

Michael Flohr

### Event

Talk given on 29. April 2004 at Department of Mathematical Sciences, University of Durham, United Kingdom.

### Sources and Abstract

A very simple explanation of logarithmic conformal field theory for third year students in only 15 minutes.

• Four-Point Functions in LCFT - Surprises from $$\boldsymbol{\mathrm{SL}(2,\mathbb{C})}$$ Covariance

### Authors

Michael Flohr (Speaker) and Marco Krohn

### Event

Talk given at the XVI. workshop Beyond the Standard Model, March 2004 at Physikzentrum Bad Honnef, Germany.

### Sources and Abstract

The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The presented algorithm is illustrated with some non-trivial examples and permutation symmetries are exploited to reduce the number of free structure-functions, which cannot be fixed by global conformal invariance alone.

• Somewhere over the Rainbow - Vom Regenbogen zur Stringtheorie

### Authors

Michael Flohr

### Event

Inaugural Lecture (in german) given on 15. October 2003 at the University of Hannover. I was then invited to give the same talk on 20. November 2003 within the physics colloquium at the University of Bonn.

### Sources and Abstract

Der Regenbogen ist ein optisches Phänomen, das auf Laien wie Wissenschaftler gleichermaßen eine tiefe Faszination ausübt. Eine vollständige und exakte physikalische Erklärung des Regenbogens gelang allerdings erst im 20. Jahrhundert.     Die Erklärungsversuche zum Regenbogen, beginnend mit Aristoteles, sind ein wunderschönes Beispiel dafür, wie Physik funktioniert. Im Vortrag werde ich mich auf diejenigen Eigenschaften des Regenbogens beschränken, die man mit dem unbewaffneten Auge sehen kann, insbesondere die Verteilung der Farben, den zweiten Regenbogen, die ALexanderspalte und die sogenannten überzählige Bögen. Jede dieser Eigenschaften wird im Laufe des Vortrages erklärt werden, wobei wir schrittweise modernere Vorstellungen über die Natur des Lichtes verwenden müssen — bis hin zur Quantenmechanik — wie auch über die Entwicklung von Regentropfen. Im letzten Teil des Vortrages diskutiere ich, wie mit Methoden der mathematischen Physik die exakte aber nur sehr schwierig zu berechnende Lösung des Regenbogenproblems handhabbar gemacht werden kann.     Wir werden im Laufe des Vortrages wiederholt Modellvorstellungen begegnen, die auch in anderen Gebiten der Physik, von der Kernphysik bis hin zur Stringtheorie, eine große Rolle spielen. Obwohl die moderne Erklärung des Regenbogens eindeutig zur fortgeschrittenen theoretischen bzw. mathematische Physik zählt, ist der Vortrag bewußt allgemeinverständlich gehalten und verzichtet fast vollständig auf Formeln.

### Lyrics

Somewhere over the rainbow, way up high,
There's a land that I heard of once in a lullaby.
Somewhere over the rainbow, skies are blue,
And the dreams that you dare to dream really do come true.

Someday I'll wish upon a star
And wake up where the clouds are far behind me.
Where troubles melt like lemon drops,
Away above the chimney tops, that's where you'll find me.

Somewhere over the rainbow, bluebirds fly.
Birds fly over the rainbow, why then oh why can't I?

Someday I'll wish upon a star
And wake up where the clouds are far behind me.
Where troubles melt like lemon drops,
Away above the chimney tops, that's where you'll find me.

Somewhere over the rainbow, bluebirds fly.
Birds fly over the rainbow, why then oh why can't I?
Birds fly over the rainbow, why then oh why can't I?

If happy little bluebirds fly beyond the rainbow,
Why oh why can't I?

(from: The Wizard of Oz)

• Recent Developments in Logarithmic Conformal Field Theory

### Authors

Michael Flohr

### Event

Invited plenary lecture on the first annual meeting of the EU Network EUCLID (EUropean Collaboration Linking Integrability with other Disciplins) Integrable Models and Applications: from Strings to Condensed Matter, September 2003 in Florence, Italy.

### Sources and Abstract

We report on recent developments in the understanding and mathematical foundation of logarithmic conformal field theory. In particular, we disucss:
1) The geometric origin of logarithmic operators for a certain class of logarithmic conformal field theories. The role of zero modes and the relation to deformations of the stress-energy tensor a la Fjelstad, Fuchs et al. are elucidated.
2) The meaning of solutions of the modular differential equation, which cannot be understood as characters (i.e. traces over representation modules), is clarified, which leads to the necessity to generalize certain notions of rationality.

pdf   ::   ogg   ::   Web Site

• Gibt es Dunkle Materie?

### Authors

Michael Flohr

### Event

Habilitation Colloquium (in german) held on 18. June 2003 at the University of Hannover.

### Sources and Abstract

In diesem Habilitations-Kolloquium geht es um die Frage, ob es Dunkle Materie wirklich gibt. Zunächst wird erörtert, warum man die Existenz von Dunkler Materie gemeinhin annimmt, wobei sowohl die astronomische Evidenz als auch kosmologische Gründe gewürdigt werden. Anschließend wird der aktuelle Stand der Suche und des dirketen experimentellen Nachweises von Dunkler Materie diskutiert.     In jedem dieser drei Teile arbeitet der Vortrag auch die bestehenden Widersprüche und Paradoxien heraus und erklärt, welche experimentellen Anstrengungen aus welchen Gründen nach wie vor keinen Erfolg gezeigt haben.     Ziel des Vortrages ist es durchaus, den überaus hypothetischen Charakter der allgemein akzeptierten These der Existenz von Dunkler Materie deutlich zu machen und aufzuzeigen, dass die gängigen Vorstellungen zur Dunklen Materie unvollständig und mit Sicherheit in ihrer derzeitigen Form fehlerhaft sein müssen.

### Lyrics

Ob zuerst das Licht da war
oder doch eher die Dunkelheit;
ob es irgendwo nichts gibt,
und ob von etwas,
wenn ihr so weitermacht,
etwas übrigbleibt,
von der guten alten Materie,
außer einer Überdosis Mathematik?

Könnt ihr mir sagen,
ob es sein Bewenden hat
mit 22 Dimensionen,
oder sollen es ein paar mehr sein?
ob das Jenseits ein Wurmloch ist,
und auf wie viele Paralleluniversen
ich mich gefaßt machen muß?

Ehrfürchtig lausche ich
euern exakten Märchen,
ihr Hohepriester.
So viele Fragen. An wen,
wenn nicht an euch,
die letzten Mohikaner
der Metaphysik,
soll ich sie richten?

(Hans Magnus Enzensberger :: Fragen an die Kosmologen)

## TALKS PRESENTED BY MY STUDENTS

• Factorization Constraints in Non–Compact Non–Rational Conformal Field Theory

### Authors

Hendrik Adorf (Speaker) and Michael Flohr

### Event

Talk given March 2008 at the XX. Workshop Beyond the Standard Model, Physikzentrum Bad Honnef, Germany.

### Sources and Abstract

We consider the $H_3^+$ model as a prototype for non-compact non-rational CFTs and study the role of sewing constraints on the D-brane spectrum. In the literature, two approaches to deal with the boundary 2-point function have been proposed: One assumes analyticity of this correlator as standard CFT axioms require, the other only continuity at certain singular points suggested by mapping the model to Liouville theory. In the first approach, the Cardy-Lewellen factorization constraints remain valid everywhere, while in the second approach, they must be weakened at the lines, where only continuity is assumed. We show explicitly that both approaches work out and lead to consistent and coinciding results. We discuss some implications of this observation.

• $$\boldsymbol{D}$$-Branes in a Non-Compact WZNW Model

### Authors

Hendrik Adorf (Speaker) and Michael Flohr

### Event

Talk given October 2007 at the University of Potsdam, Germany.

### Sources and Abstract

For $$AdS$$ boundary conditions, we give a solution of the $$H_3^+$$ two point function involving degenerate field with $$\mathrm{SL}(2)$$-label $$b^{-2}/2$$, which is defined on the full $$(u,z)$$ unit square. It consists of two patches, one for $$z < u$$ and one for $$u < z$$. Along the $$u = z$$ “singularity”, the solutions from both patches are shown to have finite limits and are merged continuously as suggested by the work of Hosomichi and Ribault. From this two point function, we can derive $$b^{-2}/2$$-shift equations for $$AdS_2$$ D-branes. We show that discrete as well as continuous $$AdS_2$$ branes are consistent with our novel shift equations without any new restrictions.

• Towards the construction of local logarithmic conformal field theories

Anne-Lý Do

### Event

Talk given July 2007 at the Max-Planck Institute for Complex Systems, Dresden, Germany.

### Sources and Abstract

Although logarithmic conformal field theories are known not to factorise many previous findings have only been formulated on their chiral halves. Making only mild and rather general assumptions on the structure of an chiral logarithmic conformal field theory we deduce statements about its local non-chiral equivalent. Two methods are presented how to construct local representations as subrepresentations of the tensor product of chiral and anti-chiral Jordan cells. Furthermore we explore the assembly of generic non-chiral correlation functions from generic chiral and anti-chiral correlators. The constraint of locality is studied and the generality of our method is discussed.

• Fermionic Expressions for the Characters of $$\boldsymbol{c_{p,1}}$$ Logarithmic Conformal Field Theories

### Authors

Michael Flohr, Carsten Grabow and Michael Koehn (Speaker) Event Talk given March 2007 at the XIX. Workshop Beyond the Standard Model, Physikzentrum Bad Honnef, Germany. Sources and Abstract

We present fermionic quasi-particle sum representations consisting of a single fundamental fermionic form for all characters of the logarithmic conformal field theory models with central charge $$c_{p,1}$$, $$p \geq 2$$, and suggest a physical interpretation. We also show that it is possible to correctly extract dilogarithm identities.

• Vertex operator algebra approach to logarithmic conformal field theory

### Authors

Nils Carqueville

### Event

Talk given June 2006 at the XVth International Colloquium on Integrable Systems and Quantum Symmetries in Prague, Czechia.

### Sources and Abstract

It is an open question whether or not it is possible to generalize the definition of a vertex operator algebra to treat logarithmic conformal field theory already at the vacuum sector. With this task in mind, universal bracket relations for logarithmic mode algebras are given.

• Vertex Algebras, Operator Product Expansion and $$\boldsymbol{C_2}$$-cofiniteness

### Authors

Nils Carqueville

### Event

Talk given February 2006 at the Max Planck Institute for Mathematics, Bonn, Germany.

### Sources

In this talk, the $$C_2$$-cofiniteness for the series of the $${\cal W}_{p,1}$$ triplet algebra logarithmic conformal field theories is established. The main focus of this talk is the mathematically rigorous definition of these logarithmic conformal field theories in terms of vertex operator algebras.

• Nonmeromorphic operator product expansion and $$\boldsymbol{C_2}$$-cofiniteness for a family of $$\boldsymbol{{\cal W}}$$-algebras

### Authors

Nils Carqueville

### Event

Talk given December 2005 at the 17. Workshop Foundations and Constructive Aspects of Quantum Field Theory, University of Göttingen, Germany.

### Sources and Abstract

In this talk, the $$C_2$$-cofiniteness for the series of the $${\cal W}_{p,1}$$ triplet algebra logarithmic conformal field theories is established.

• Explicit formulas for the scalar modes in Seiberg-Witten theory

### Authors

Nikolas Akerblom (Speaker) and Michael Flohr

### Event and Abstract

Talk given March 2005 at the XVII. Workshop Beyond the Standard Model, Physikzentrum Bad Honnef, Germany.

### Sources

General formulas for the scalar modes $$a_i$$ and $$a_D^{\ \ \ i}$$ in the Seiberg-Witten $$\mathrm{SU}(N)$$ setting are derived in terms of the $$F_D^{(n)}$$-type Lauricella functions in the cases with and without massive hypermultiplets. Subsequently these formulas are applied in a study of the $$\mathrm{SU}(3)$$ Argyres-Douglas point. We use this example to study the question, whether the scalar modes admit an interpretation in terms of BPS mass states everywhere in moduli space.