# Correct links are attached. Sorry for the inconvenience. # (updated on March 2022)
Recordings
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The links to recordings of the 1st week are listed below.
"Lecture by I.Sachs"
"Lecture by B.Jurco"
"Lecture by M.Wolf"
"Lecture by C.Saemann"
"Lecture by K.Itoh"
"Lecture by T.R.Morris"
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The links to recordings of the 2nd week are listed below.
"Talks 1-1 (March 29)"
"Talks 1-2 (March 29)"
"Talks 1-3 (March 29)"
"Talks 2-1 (March 30)"
"Talks 2-2 (March 30)"
"Talks 2-3 (March 30)"
"Talks 2-1 (March 31)"
"Talks 2-2 (March 31)"
"Talks 2-3 (March 31)"
[ 1st week ]
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The Zoom URL was sent to participants.
If you have not received the Zoom URL yet, please contact us.
- The lecture slides and recordings are now available.
Lecture Schedule
| Mar. 24 (Wed) | Mar. 25 (Thu) | Mar. 26 (Fri) | Mar. 27 (Sat) | ||
|---|---|---|---|---|---|
| UTC 9:00~12:00 |
CET 10:00~13:00 |
18:00~22:00 I.Sachs & B.Jurco |
18:00~21:00 M.Wolf |
18:00~21:00 C.Saemann |
18:00~21:00 K.Itoh & T.R.Morris |
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The above schedule is just a rough standard:
Lecture time will be extended or shortened at lecturer's discretion. - Lecture time includes break time.
March 24 (18:00~22:00 JST)
- Ivo Sachs (Arnold Sommerfeld Center, LMU Munich)
Lecture Title:
"Homotopy Algebras and String Theory"
Abstract:
Any BV-BRST gauge theory gives rise to a homotopy algebra, canonically upon expansion around a critical point. In string theory we don’t have a gauge theory to start with, but instead the homotopy structure arises geometrically which can the be exploited to construct a string field theory action perturbatively and world-sheet string theory as its minimal model.
- Branislav Jurco (Math. Inst., Charles Univ. Prague)
Lecture Title:
"Operads and String Field Theory homotopy algebras"
Abstract:
This will be an introductory lecture about the operadic origin of algebraic structures of SFT.
March 25 (18:00~21:00 JST)
- Martin Wolf (Dept. Math., Univ. Surrey)
Lecture Title: "Introduction to the BV formalism and homotopy algebras"
March 26 (18:00~21:00 JST)
- Christian Saemann (Maxwell Inst. & Heriot-Watt Univ., Edinburgh)
Lecture Title:
"Scattering amplitudes and Feynman diagrams from homotopy algebras"
March 27 (18:00~22:00 JST)
- Katsumi Itoh (Niigata Univ.)
Lecture Title:
"Realization of symmetry in the ERG approach to QFT"
Abstract:
We review the exact renormalization group approach to QFT. The talk consist of three parts. 1) In ERG, a field theory is constructed by starting from a path integral with a momentum cutoff. Its basic formalism is explained for a scalar field theory and the perturbative renormalizability is discussed. 2) We show that the Batalin-Vilkovisky formalism is a powerful tool to describe the modified form of gauge symmetry realized in the presence of the cutoff. 3) The dimensionless flow equation is introduced to find a phase structure. In closing the talk, we mention the remaining difficult problems associated with gauge symmetry in ERG.
- Tim R Morris (Dept. Phys.&Astr., Univ. Southampton)
Lecture Title:
"BRST in the ERG"
Abstract:
The Quantum Master Equation and the Wilsonian Exact Renormalization Group flow equation can be combined such that for the continuum effective action, quantum BRST invariance is not broken by the presence of an effective ultraviolet cutoff, Lambda, despite the fact that the structure demands quantum corrections that naively break the gauge invariance, such as a mass term for a non-Abelian gauge field. Exploiting the derivative expansion, BRST cohomological methods fix the solution up to choice of renormalization conditions, without inputting the form of the classical, or bare, interactions. Legendre transformation results in an equivalent description in terms of solving the modified Slavnov-Taylor identities and the flow of the Legendre effective action under an infrared cutoff, Lambda. The flow generates a canonical transformation that automatically solves the Slavnov-Taylor identities for the wavefunction renormalization constants. This structure is illustrated using perturbation theory in Yang-Mills and quantum gravity.
[ 2nd week ]
- Please check your time zone. (JST schedule is most reliable.)
- Some of the talk slides are now available: the other slides may be available later.
Talk Program
| UTC | BST/CET | CEST | Mar. 29 (Mon) | Mar. 30 (Tue) | Mar. 31 (Wed) |
|---|---|---|---|---|---|
| 7:30~8:30 |
8:30~9:30 |
9:30~10:30 |
16:30~17:00 H.Kajiura 17:00~17:30 H.Matsunaga |
16:30~17:00 Y.Okawa 17:00~17:30 T.Erler |
16:30~17:00 Y.Igarashi 17:00~17:30 N.Ikeda |
| 9:00~10:30 |
10:00~11:30 |
11:00~12:30 |
18:00~18:30 A.Arvanitakis 18:30~19:00 J.Pulmann 19:00~19:30 O.Hohm |
18:00~18:30 I.Saberi 18:30~19:00 I.Sachs 19:00~19:30 B.Jurco |
18:00~18:45 L.Borsten 18:45~19:30 H.Kim |
| 11:00~12:00 |
12:00~13:00 |
13:00~14:00 |
20:00~20:30 C.Saemann 20:30~ Discussion |
20:00~20:30 T.R.Morris 20:30~ Discussion |
20:00~20:45 T.Macrelli 20:45~ Discussion |
March 29 (Mon)
- 16:30-17:00 Hiroshige Kajiura (Chiba univ.)
Talk Title:
"Homological perturbation theory in homological mirror symmetry"
Abstract:
We explain Kontsevich-Soibelman's proposal of understanding homological mirror symmetry by homological perturbation theory of A-infinity algebras. We apply it to homological mirror symmetry of tori and derive the A-infinity products of the Fukaya category explicitly. We also generalize this framework to toric manifolds which is a recent collaboration with M. Futaki.
- 17:00-17:30 Hiroaki Matsunaga (YITP, Kyoto univ. / Charles univ.)
Talk Title:
"Homotopy algebra and symmetry generators in QFT"
Abstract:
We explain how a homotopy algebraic structure arises in realization of symmetry generators and show that it is preserved under the perturbative path-integral. We see that nonlinear realizations of symmetries in "effective field theories" can be read from this homotopy algebraic structure.
- 18:00-18:30 Alexandros Spyridon Arvanitakis (Vrije Universiteit Brussel)
Talk Title:
"(Beyond) Effective Field Theory with Homotopy Transfer"
Abstract:
I will review the L-infinity algebra formulation of classical field theory and introduce a more recent version that also accommodates quantum field theories using Zinn-Justin's formulation of QFT. On the mathematical side, this gives a novel construction of an ordinary L-infinity algebra from a "loop" one. I will then explain how the algebraic operation of homotopy transfer generalises Wilsonian effective field theory, and outline an application of this idea to the "double field theory" describing the dynamics of massless string states on the doubled torus.
- 18:30-19:00 Jan Pulmann (Univ. Geneva)
Talk Title:
"Connected sum and Beilinson-Drinfeld algebras"
Abstract:
Modular operads relevant to string theory can be equipped with an additional structure, coming from the connected sum of surfaces. We show how this structure gives rise to a commutative product on the space of functions associated to the modular operad. Together with the usual non-commutative BV structure present on this space of functions, the commutative product forms a Beilinson-Drinfeld algebra, a close cousin of a BV algebra. Based on a join work with Martin Doubek, Branislav Jurco and Lada Peksova.
- 19:00-19:30 Olaf Hohm (Humboldt University, Berlin)
Talk Title:
"Gauge invariant perturbation theory via homotopy transfer"
Abstract:
Methods developed in cosmological perturbation theory to define gauge invariant variables can be interpreted in terms of homotopy transfer. This in turn gives an algorithmic procedure to define gauge invariant variables to all orders in fluctuations.
- 20:00-20:30 Christian Saemann (Maxwell Inst. & Heriot-Watt Univ., Edinburgh)
Talk Title:
"EL_infinity-algebras and applications"
Abstract:
In this talk, I will introduce a new type of homotopy algebras that generalize L_infinity-algebras and that appear naturally in many contexts within mathematics and physics. I will sketch a number of applications, ranging from generalized geometry to gauged supergravity and higher gauge theory.
March 30 (Tue)
- 16:30-17:00 Yuji Okawa (Univ. Tokyo)
Talk Title:
"Gauge-invariant operators of open bosonic string field theory in the low-energy limit"
Abstract:
In the AdS/CFT correspondence we consider correlation functions of gauge-invariant operators on the gauge theory side, which we obtain in the low-energy limit of the open string sector. To investigate this low-energy limit we consider the action of open bosonic string field theory including source terms for gauge-invariant operators and classically integrate out massive fields to obtain the effective action for massless fields. While the gauge-invariant operators depend linearly on the open string field and do not resemble the corresponding operators such as the energy-momentum tensor in the low-energy limit, we find that nonlinear dependence is generated in the process of integrating out massive fields. We also find that the gauge transformation is modified in such a way that the effective action and the modified gauge transformation can be written in terms of the same set of multi-string products which satisfy weak $A_\infty$ relations, and we present explicit expressions for the multi-string products. The talk is based on arXiv:2006.16710 in collaboration with Daiki Koyama and Nanami Suzuki.
- 17:00-17:30 Theodore Erler (Inst. Phys., Czech Academy of Sci.)
Talk Title:
"Lightcone gauge in covariant string field theory"
Abstract:
In this talk we will describe how to fix lightcone gauge in covariant string field theories. In particular, this leads to a mapping of the field variables of Witten's open bosonic string field theory and Kaku and Kikkawa's lightcone string field theory.
- 18:00-18:30 Ingmar Saberi (LMU Munich)
Talk Title:
"A presymplectic BV formalism for the abelian (2,0) tensor multiplet"
Abstract:
The tensor multiplet of six-dimensional N=(2,0) supersymmetry, which is related to the worldvolume theory of a single M5 brane, famously includes a self-dual two-form. Direct computations in this theory, including a description of its twists, have been rendered difficult by the absence of any standard Lagrangian formulation for such fields. We give a classical description of the two possible twists, using a perturbative formulation of the free theory which is motivated by the pure spinor superfield formalism; fully understanding this formulation requires broadening one's notion of BV theory to allow for degenerate shifted symplectic structures. Just as for the tensor multiplet itself, the twisted theories are presymplectic BV theories that are holomorphic or holomorphic-topological. I'll comment on both the successes of this approach and some points where further understanding is needed, as well as on some surprising connections to other issues including electric-magnetic duality.
- 18:30-19:00 Ivo Sachs (LMU Munich)
Talk Title:
"BRST-BV field theories fom graded Lie-algebras"
Abstract:
Starting form a suitable reduction of the graded Lie super algebra of the spinning particle we construct a geometric BV-BRST gauge system as an approximation to a background independent string field theory as a theory of background fields.
- 19:00-19:30 Branislav Jurco (Math. Inst., Charles Univ., Prague)
Talk Title:
"Some remarks on HPL"
Abstract:
We discuss some topics related to HPL like homotopies and morphisms of (quantum) homotopy algebras.
- 20:00-20:30 Tim R Morris (Univ. Southampton)
Talk Title:
"Quantum gravity, diffeomorphism invariance and a perturbative continuum limit"
Abstract:
We show that the Wilsonian renormalization group (RG) provides a natural regularisation of the Quantum Master Equation such that to first order the BRST algebra closes on local functionals spanned by the eigenoperators with constant couplings. We then apply this to quantum gravity. Wilsonian RG properties of the conformal factor of the metric are profoundly altered by the fact that it has a wrong-sign kinetic term. The result is a novel perturbative continuum limit for quantum gravity, which is however non-perturbative in Planck?s constant. The renormalized trajectory emanates from the Gaussian fixed point but enters the diffeomorphism invariant subspace only well below a dynamically generated scale. To second order in perturbation theory, the result is the same as computed in the standard quantisation. Although this case is renormalizable at second order for kinematic reasons, the structure we uncover works in general.
March 31 (Wed)
- 16:30-17:00 Yuji Igarashi (Niigata univ.)
Talk Title:
"QED in the exact renormalization group"
Abstract:
We discuss the compatibility of the RG flow equation and the regularized gauge symmetry, expressed as the quantum master equation, for a chiral invariant QED with 4-fermi interaction. We explain how the gauge symmetry is realized in the presence of the momentum cutoff as well as 4-fermi interactions.
- 17:00-17:30 Noriaki Ikeda (Ritsumeikan univ.)
Talk Title:
"BV and BFV for the H-twisted Poisson sigma model"
Abstract:
We present the BFV and the BV extension of the Poisson sigma model (PSM) twisted by a closed 3-form H. There exist superfield versions of these functionals such as for the PSM and, more generally, for the AKSZ sigma models. However, in contrast to those theories, they depend on the Euler vector field of the source manifold and contain terms mixing data from the source and the target manifold.
We obtain purely geometrical expressions, which are new also for the ordinary PSM and promise adaptations to other Lie algebroid based gauge theories: The BV functional is the sum of the classical action, the Hamiltonian lift of the (only on-shell-nilpotent) BRST differential, and a term quadratic in the antifields which is essentially the basic curvature and measures the compatibility of a connection $ abla$ with the Lie algebroid structure on the cotangent bundle over the target space M.
- 18:00-18:45 Leron Borsten (MIMS, Heriot-Watt univ.)
Talk Title:
"BV double copy from homotopy algebras. Part 0"
Abstract:
Double copy is a deep relationship between the scattering amplitudes of Yang-Mills and those of Einstein gravity, descending from KLT relations in string theory. Although the double copy is known to hold for tree-level amplitudes, the loop case has been a longstanding conjecture. In this series of two talks, we argue that the double-copy relation holds to all orders, tree and loop. To do so, we take a Lagrangian point of view in terms of BV-gauge-fixed actions associated to cyclic homotopy (A-, L-, or C-infinity) algebras.
Based on 2007.13803 and 2102.11390, joint work by L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, M. Wolf.
- 18:45-19:30 Hyungrok Kim (MIMS, Heriot-Watt univ.)
Talk Title:
"BV double copy from homotopy algebras. Part 1"
Abstract:
Double copy is a deep relationship between the scattering amplitudes of Yang-Mills and those of Einstein gravity, descending from KLT relations in string theory. Although the double copy is known to hold for tree-level amplitudes, the loop case has been a longstanding conjecture. In this series of two talks, we argue that the double-copy relation holds to all orders, tree and loop. To do so, we take a Lagrangian point of view in terms of BV-gauge-fixed actions associated to cyclic homotopy (A-, L-, or C-infinity) algebras.
Based on 2007.13803 and 2102.11390, joint work by L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, M. Wolf.
- 20:00-20:45 Tommaso Macrelli (University of Surrey)
Talk Title:
"BV double copy from homotopy algebras. Part 2"
Abstract:
Double copy is a deep relationship between the scattering amplitudes of Yang-Mills and those of Einstein gravity, descending from KLT relations in string theory. Although the double copy is known to hold for tree-level amplitudes, the loop case has been a longstanding conjecture. In this series of two talks, we argue that the double-copy relation holds to all orders, tree and loop. To do so, we take a Lagrangian point of view in terms of BV-gauge-fixed actions associated to cyclic homotopy (A-, L-, or C-infinity) algebras.
Based on 2007.13803 and 2102.11390, joint work by L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, M. Wolf.
The time schedule is based on the Japanese Standard Time (JST)
JST = UTC+9 = CET+8 = BST+8 = CEST+7
Please notice that SUMMER TIME may start from March 28.
Please notice that SUMMER TIME may start from March 28.