# “QFT, Strings and Beyond”

## Fall Semester 2021

Tuesday, 14:00, HIT E41.1

Organised by: Niklas Beisert, Johannes Broedel, Matthias Gaberdiel, Marc-Antoine Fiset, Pietro Longhi

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Wed

22.09.

14:00

HIT E41.1

Nana Cabo Bizet (Universidad de Guanajuato)

“The geometry of gauged linear sigma models and T-duality”

abstract (click to view)
Mirror symmetry constitutes a correspondence between two different Calabi-Yau varieties M and W, such that compactifications of type IIA and type IIB string theory on them, give rise to equivalent physics. The gauged linear sigma models (GLSM) constitute an UV description of the string world-sheet theory. Abelian T-duality in GLSMs has been proven to be equivalent to mirror symmetry. We construct non-Abelian T-dualities in GLSMs, exploring the geometry of the dual models. We discuss the duality for a supersymmetric (2,2) GLSM whose vacuum is given by the deformed conifold. This is a model with SU(2)xSU(2) global symmetry which is gauged to obtain a Lagrangian that allows to interpolate between dual models. These dualities give rise to new physical equivalences. (click to hide)

Tue

28.09.

14:00

HIT E41.1

Marius Gerbershagen (Universität Würzburg)

“Generalized entanglement measures in AdS3/CFT2”

abstract (click to view)
In the AdS/CFT context, generalized entanglement refers to an entanglement measure that takes into account not only quantum correlations between between spatial degrees of freedom, but also between different fields of the theory. In this talk, I will explain how to define one such entanglement measure in AdS3/CFT2 that is dual to the length of a geodesic winding around a naked singularity or black hole horizon. I will discuss the computation of this quantity for pure states dual to conical defects and thermal states dual to BTZ black hole backgrounds in the D1/D5 system at the orbifold point as well as subtleties regarding its gauge invariant definition. Finally, I will comment on deformations away from the orbifold point and consequences for the reconstruction of the bulk geometry in terms of boundary data. (click to hide)

Tue

05.10.

14:00

HIT E41.1

Tommaso Macrelli (ETH)

“Colour-kinematic duality, double copy and homotopy algebras”

abstract (click to view)
While colour-kinematic duality and double copy are a well established paradigm at tree level, their loop level generalisation remained for a long time an unsolved problem. Lifting the on-shell, scattering amplitude-based description to an action-based approach, we show that a theory that exhibits tree level colour-kinematic duality can be reformulated in a way such that its loop integrands manifest colour-kinematic duality.

With Yang-Mills theory as our main example, we provide a theoretical toolkit for systematically producing a loop level colour-kinematic duality manifesting action from a theory with colour-kinematic-dual tree level scattering amplitudes. Finally, we discuss an interpretation of colour-kinematic duality and double copy in terms of homotopy algebras, introducing an adequate notion of colour-kinematic factorisation.

This talk is based on arXiv:2007.13803 [hep-th], arXiv:2102.11390 [hep-th], arXiv:2108.03030 [hep-th]. (click to hide)

With Yang-Mills theory as our main example, we provide a theoretical toolkit for systematically producing a loop level colour-kinematic duality manifesting action from a theory with colour-kinematic-dual tree level scattering amplitudes. Finally, we discuss an interpretation of colour-kinematic duality and double copy in terms of homotopy algebras, introducing an adequate notion of colour-kinematic factorisation.

This talk is based on arXiv:2007.13803 [hep-th], arXiv:2102.11390 [hep-th], arXiv:2108.03030 [hep-th]. (click to hide)

Tue

19.10.

17:00

Grant Remmen (UCSB)

“Amplitudes and the Riemann Zeta Function” (UNUSUAL TIME)

abstract (click to view)
In this talk, I will connect physical properties of scattering amplitudes to the Riemann zeta function. Specifically, I will construct a closed-form amplitude, describing the tree-level exchange of a tower with masses m^2_n = \mu^2_n, where \zeta(\frac{1}{2}\pm i \mu_n) = 0. Requiring real masses corresponds to the Riemann hypothesis, locality of the amplitude to meromorphicity of the zeta function, and universal coupling between massive and massless states to simplicity of the zeros of \zeta. Unitarity bounds from dispersion relations for the forward amplitude translate to positivity of the odd moments of the sequence of 1/\mu^2_n (click to hide)

Tue

26.10.

14:00

HIT E41.1

Albrecht Klemm (Universitat Bonn)

“Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives”

abstract (click to view)
We provide a summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the example of multi-loop banana integrals. For example, we show how Griffiths transversality, known from the theory of variation of mixed Hodge structures, leads quite generically to a set of quadratic relations among maximal cut integrals associated to Calabi-Yau motives. These quadratic relations then naturally lead to a compact expression for $l$-loop banana integrals in $D=2$ dimensions in terms of an integral over a period of a Calabi-Yau $(l-1)$-fold. This new integral representation generalizes in a natural way the known representations for $l\le 3$ involving logarithms with square root arguments and iterated integrals of Eisenstein series. We show how the results can be extended to dimensional regularization. We present a method to obtain the differential equations for banana integrals with an arbitrary number of loops in dimensional regularization without the need to solve integration-by-parts relations. We also present a compact formula for the leading asymptotics of banana integrals with an arbitrary number of loops in the large momentum limit that generalizes the $\widehat{\Gamma}$-class formalism to dimensional regularization and provides a convenient boundary condition to solve the differential equations for the banana integrals. As an application, we present for the first time numerical results for equal-mass banana integrals with up to four loops and up to second order in the dimensional regulator. (click to hide)

Tue

26.10.

15:00

HIT E41.1

Michael Borinsky, Johannes Broedel, Albrecht Klemm

“From Feynman graphs to Calabi-Yau manifolds” (Block seminars 3pm-6pm)

Wed

27.10.

14:00

HIT E41.1

Michael Borinsky, Johannes Broedel, Albrecht Klemm

“From Feynman graphs to Calabi-Yau manifolds” (Block seminars 2pm-6pm)

Wed

03.11.

14:00

HIT E41.1

Lorenzo Bianchi (Università di Torino)

“A Page curve from boundary quenches” (UNUSUAL DAY)

abstract (click to view)
In light of the recent progress in understanding the black hole information paradox, we consider a local quench in a boundary conformal field theory and study the entropy of the emitted radiation. We show that the real time evolution has the features of a Page curve (the entropy grows at early time and decays at late time). We provide a general upper bound on the late time behaviour of the entanglement entropy and we show that this bound is saturated by the holographic result. We conclude by commenting on how this setup is related to black hole radiation. (click to hide)

Tue

09.11.

14:00

Leron Borsten (Heriot-Watt University, Edinburgh)

“On colour-kinematic duality and the double copy”

abstract (click to view)
We begin by reviewing the colour-kinematics duality of (super) Yang-Mills theory and its double copy into (super)gravity. We then show that off-shell colour-kinematics duality can be made manifest in the Yang—Mills Batalin—Vilkovisky action, up to Jacobian counter-terms. The latter imply a departure from what is normally understood by colour-kinematics duality in that the counterterms generically break it. However, this notion of CK duality is very natural and, most importantly, implies the validity of the double copy to all orders in perturbations theory. We then describe generalisations to the non-linear sigma model and super Yang-Mills theory, where Sen’s formalism for self-dual field strengths emerges automatically. We conclude by discussing the mathematical underpinnings of these observations in terms of Homotopy algebras. Figuratively, colour-kinematics duality is a symmetry of Yang—Mills in the same sense that a mug is a donut. (click to hide)

Tue

16.11.

14:00

Roberto Ruiz Gil (Universidad Complutense de Madrid)

“Wess-Zumino-Novikov-Witten spin-chain σ-models”

abstract (click to view)
In this talk, I shall present the spin-chain σ-model of the Wess-Zumino-Novikov-Witten (WZNW) model that realises bosonic strings on AdS3 x S3 with pure Neveu-Schwarz-Neveu-Schwarz flux. I shall begin with a review of developments made in the AdS5/CFT4 correspondence on the basis of spin-chain σ-models. I shall then focus on spin-chain σ-models for the SL(2,R) and SU(2) WZNW models. I shall present their construction from both a semi-classical limit in the classical action and a Landau-Lifshitz limit in the underlying integrable spin chain. I shall finish by commenting on open problems. (click to hide)

Tue

23.11.

14:00

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Elli Pomoni (DESY)

“Dynamical spin chains in 4D N = 2 SCFTs”

abstract (click to view)
In this talk we will revisit the study of spin chains capturing the spectral problem of 4d N = 2 SCFTs in the planar limit. At one loop and in the quantum plane limit, we will discover a quasi-Hopf symmetry algebra, defined by the R-matrix read off from the superpotential. This implies that when orbifolding the N = 4 symmetry algebra down to the N = 2 one and then marginaly deforming, the broken generators are not lost, but get upgraded to quantum generators. Thereafter, we will demonstrate that these chains are dynamical, in the sense that their Hamiltonian depends on a parameter which is dynamically determined along the chain. At one loop we will show how to map the holomorphic SU(3) scalar sector to a dynamical 15-vertex model, which corresponds to an RSOS model, whose adjacency graph can be read off from the gauge theory quiver/brane tiling. One scalar SU(2) sub-sector is described by an alternating nearest-neighbour Hamiltonian, while another choice of SU(2) sub-sector leads to a dynamical dilute Temperley-Lieb model. These sectors have a common vacuum state, around which the magnon dispersion relations are naturally uniformised by elliptic functions. For the example of the SU(N)xSU(N) quiver theory we will study these dynamical chains by solving the one- and two-magnon problems with the coordinate Bethe ansatz approach. (click to hide)

Tue

30.11.

14:00

HIT E41.1

Carlo Maccaferri (Università di Torino)

“Background Independence of Open String Field Theory”

abstract (click to view)
I review the recent construction of analytic classical solutions of open string field theory (OSFT) which describe any boundary conformal field theory (BCFT) as a solution of the OSFT defined on any other BCFT. This establishes that all D-branes are open string solitons of the same space-time theory. The theory of fluctuations on the classical solution can be related to the OSFT directly defined on the new D-brane system by integrating out certain pure gauge degrees of freedom and then by performing a simple field redefinition. I give an explicit construction of this integration-out via a novel application of the homotopy transfer in the framework of the homological perturbation lemma. (click to hide)

Tue

07.12.

14:00

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David Tennyson (Imperial College London)

“Topological strings at 1-loop from double complexes”

abstract (click to view)
The topological A/B-model have been important tools for studying both string theory and the geometry of Calabi-Yau manifolds. They provide both new geometric invariants of the Calabi-Yau, as well as calculating certain terms in the effective theory of string theory. While topological strings on other special holonomy manifolds have been postulated, they are far less understood. In my talk, I will examine the topological string on G2 and Spin(7) manifolds from the target space perspective. I will show that any special holonomy manifold has a double complex which generalises the Dolbeault complex of Calabi-Yau manifolds and provides the natural candidate for the BRST complex of the topological string. Through this, I will be able to conjecture the cohomology of operators and the 1-loop partition functions of the G2 and Spin(7) topological strings. (click to hide)

last modified: Mon, 6 Dec 2021, 15:04 CET