Bethe Algebra using Pure Spinors
Authors: Simon Ekhammar, Dmytro Volin
Preprint number: UUITP-19/21
Abstract: We propose a gl(r)-covariant parameterisation of Bethe algebra appearing in so(2r) integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials.
The Eikonal Approach to Gravitational Scattering and Radiation at O(G^3)
Authors: Paolo di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano
Preprint number: UUITP-18/21
Abstract: Using N=8 supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its non-relativistic (NR) and ultra-relativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential sub-region. This task is efficiently carried out by using the method of differential equations with complete near-static boundary conditions. In contrast to the potential-region result, the physical deflection angle includes radiation-reaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energy-momentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic tree-level amplitude, we are able to treat N=8 and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein's gravity by the addition of the radiation-reaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.
Scattering Massive String Resonances through Field-Theory Methods
Authors: Max Guillen, Henrik Johansson, Renann Lipinski Jusinskas, Oliver Schlotterer
Preprint number: UUITP-17/21
Abstract: We present a new method, exact in alpha', to explicitly compute string tree-level amplitudes involving one massive state and any number of massless ones. This construction relies on the so-called twisted heterotic string, which admits only gauge multiplets, a gravitational multiplet, and a single massive supermultiplet in its spectrum. In this simplified model, we determine the moduli-space integrand of all amplitudes with one massive state using Berends-Giele currents of the gauge multiplet. These integrands are then straightforwardly mapped to gravitational amplitudes in the twisted heterotic string and to the corresponding massive amplitudes of the conventional type-I and type-II superstrings.
Monodromy Defects in Free Field Theories
Authors: Lorenzo Bianchi, Adam Chalabi, Vladimír Procházka, Brandon Robinson, and
Preprint number: UUITP 16/21
Abstract: We study co-dimension two monodromy defects in theories of conformally
coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this
family of conformal defects by computing the one-point functions of the stress-tensor and
conserved current for Abelian flavour symmetries as well as two-point functions of the
displacement operator. In the case of d = 4, the normalisation of these correlation functions
are related to defect Weyl anomaly coefficients, and thus provide crucial information about
the defect conformal field theory. We provide explicit checks on the values of the defect
central charges by calculating the universal part of the defect contribution to entanglement
entropy. Moreover, we leverage the non-supersymmetric free field results to compute a
novel defect Weyl anomaly coefficient in a d = 4 theory of free N = 2 hypermultiplets.
In carefully studying the defect operator product expansion, we identify notable relevant
operators in the defect theories and use them to study the behaviour of the defect under
renormalisation group flow.
Curing with hemlock: escaping the swampland using instabilities from string theory
Authors: Souvik Banerjee, Ulf Danielsson, Suvendu Giri
Preprint number: UUITP-15/21
Abstract: In this essay we will take a wonderful ride on a dark bubble with strings attached, which carries our universe out of the swampland and makes it realizable in the landscape of string theory. To find the way to the landscape, we make use of apparently hostile corners of the swampland and their instabilities.
Kinematic numerators from the worldsheet: cubic trees from labelled trees
Authors: Linghui Hou, Song He, Jintian Tian and Yong Zhang
Preprint number: UUITP-14/21
Abstract: In this note we revisit the problem of explicitly computing tree-level scatter-ing amplitudes in various theories in any dimension from worldsheet formulas. The latterare known to produce cubic-tree expansion of tree amplitudes with kinematic numeratorsautomatically satisfying Jacobi-identities, once any half-integrand on the worldsheet is re-duced to logarithmic functions. We review a natural class of worldsheet functions called“Cayley functions”, which are in one-to-one correspondence with labelled trees, and natu-ral expansions of known half-integrands onto them with coefficients that are particularlycompact building blocks of kinematic numerators. We present a general formula expressingthe kinematic numerator of any cubic tree as a linear combination of these coefficients oflabelled trees, including the usual combination in terms of master numerators as a specialcase. Our results provide an efficient algorithm, which is implemented in aMathemat-icapackage, for computing tree amplitudes in non-linear sigma model, special Galileon,Yang-Mills-scalar, Einstein-Yang-Mills, Dirac-Born-Infeld and so on.
Generalized Vanishing Theorems for Yukawa Couplings in Heterotic Compactifications
Authors: Lara B. Anderson, James Gray, Magdalena Larfors, Matthew Magill, Robin Schneider
Preprint number: UUITP-13/21
Abstract: Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results in the literature used differential geometric methods to explain the origin of some of this structure. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.
Playing with the index of M-theory
Authors: Michele del Zotto, Nikita Nekrasov, Nicolo Piazzalunga, Maxim Zabzine
Preprint number: UUITP-12/21
Abstract: Motivated by M-theory, we study rank n K-theoretic Donaldson-Thomas theory on a toric threefold X. In the presence of compact four-cycles, we discuss how to include the contribution of D4-branes wrapping them. Combining this with a simple assumption on the (in)dependence on Coulomb moduli in the 7d theory, we show that the partition function factorizes and, when X is Calabi-Yau and it admits an ADE ruling, it reproduces the 5d master formula for the geometrically engineered theory on A(n-1) ALE space, thus extending the usual geometric engineering dictionary to n>1. We finally speculate about implications for instanton counting on Taub-NUT.
Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions
Authors: Paul-Konstantin Oehlmann
Preprint number: UUITP-11/21
Abstract: In this note we consider smooth elliptic Calabi-Yau four-folds whose fiber ceases to be flat over compact Riemann surfaces of genus g in the base. These non-flat fibers contribute Kähler moduli to the four-fold but also add to the three-form cohomology for g>0. In F-/M-theory these sectors are to be interpreted as compactifications of six/five dimensional N=(1,0) superconformal matter theories. The three-form cohomology leads to additional chiral singlets proportional to the dimension of five dimensional Coulomb branch of those sectors. We construct explicit examples for E-string theories as well as higher rank cases. For the E-string theories we further investigate conifold transitions that remove those non-flat fibers. First, we show how non-flat fibers can be deformed from curves down to isolated points in the base. This removes the chiral singlet of the three-forms and leads to non-perturbative four-point couplings among matter fields which can be understood as remnants of the former E-string. Alternatively, the non-flat fibers can be avoided by performing birational base changes, analogous to 6D tensor branches. For compact bases these transitions alternate all Hodge numbers but leave the Euler number invariant.
Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
Authors: Laurentiu Rodina, Zhewei Yin
Preprint number: UUITP-10/21
Abstract: We generalize soft theorems of the nonlinear sigma model beyond the O(p^2) amplitudes and the coset of SU(N)×SU(N)/SU(N). We first discuss the flavor ordering of the amplitudes for the Nambu-Goldstone bosons of a general symmetry group representation, so that we can reinterpret the known O(p^2) single soft theorem for SU(N)×SU(N)/SU(N) in the context of a general group representation. We then investigate the special case of the fundamental representation of SO(N), where a special flavor ordering of the "pair basis" is available. We provide novel amplitude relations and a Cachazo-He-Yuan formula for such a basis, and derive the corresponding single soft theorem. Next, we extend the single soft theorem for a general group representation to O(p^4), where for at least two specific choices of the O(p^4) operators, the leading non-vanishing pieces can be interpreted as new extended theory amplitudes involving bi-adjoint scalars, and the corresponding soft factors are the same as at O(p^2). Finally, we compute the general formula for the double soft theorem, valid to all derivative orders, where the leading part in the soft momenta is fixed by the O(p^2) Lagrangian, while any possible corrections to the subleading part are determined by the O(p^4) Lagrangian alone. Higher order terms in the derivative expansion do not contribute any new corrections to the double soft theorem.
Virasoro constraints revisited
Authors: Luca Cassia, Rebecca Lodin and Maxim Zabzine
Preprint number: UUITP-09/21
Abstract: We revisit the Virasoro constraints and explore the relation to the Hirota bilinear equations. We furthermore investigate and provide the solution to non-homogeneous Virasoro constraints, namely those coming from matrix models whose domain of integration has boundaries. In particular, we provide the example of Hermitean matrices with positive eigenvalues in which case one can find a solution by induction on the rank of the matrix model.
Coaction and double-copy properties of configuration-space integrals at genus zero
Authors: Ruth Britto, Sebastian Mizera, Carlos Rodriguez, Oliver Schlotterer
Preprint number: UUITP-08/21
Abstract: We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai--Lewellen--Tye relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tension alpha' or the dimensional-regularization parameter epsilon. Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of two-dimensional conformal field theories. We find a non-trivial example of correlation functions in (p,2) minimal models, which can be normalized to become uniformly transcendental in the p -> \infty limit.
Fusion of conformal defects in four dimensions
Authors: Alexander Söderberg
Preprint number: UUITP-07/21
Abstract: We consider two conformal defects close to each other in a free theory, and study what happens as the distance between them goes to zero. This limit is the same as zooming out, and the two defects have fused to another defect. As we zoom in we find a non-conformal effective action for the fused defect. Among other things this means that we cannot in general decompose the two-point correlator of two defects in terms of other conformal defects. We prove the fusion using the path integral formalism by treating the defects as sources for a scalar in the bulk.
Almost contact structures on manifolds with a G2 structure
Authors: Xenia de la Ossa, Magdalena Larfors, Matthew Magill
Preprint number: UUITP-06/21
Abstract: We review the construction of almost contact metric (three-) structures on manifolds with a G2 structure. These are of interest for certain supersymmetric configurations in string and M-theory. We compute the torsion of the SU(3) structure associated to an ACMS and apply these computations to heterotic G2 systems and supersymmetry enhancement. We initiate the study of the space of ACM3Ss, which is an infinite dimensional space with a local product structure and interesting topological features. Tantalising links between ACM3Ss and associative and coassociative submanifolds are observed.
Dark bubbles and black holes
Authors: Souvik Banerjee, Ulf Danielsson, Suvendu Giri
Preprint number: UUITP-05/21
Abstract: In this paper we study shells of matter and black holes on the expanding bubbles realizing de Sitter space, that were proposed in arXiv:1807.01570. The explicit solutions that we find for the black holes, can also be used to construct Randall-Sundrum braneworld black holes in four dimensions.
Exploring SU(N) adjoint correlators in 3d
Authors: Andrea Manenti, Alessandro Vichi
Preprint number: UUITP-04/21
Abstract: We use numerical bootstrap techniques to study correlation functions of scalars transforming in the adjoint representation of SU(N). We obtain upper bounds on operator dimensions for all the relevant representations and several values of $N$. We discover several families of kinks, which do not correspond to any known model and we discuss possible candidates. We then specialize to the case N=3,4, which has been conjectured to describe a phase transition respectively in the non compact complex projective space NCCP^2 and the antiferromagnetic complex projective model ACP^3. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to a closed region overlapping with the lattice prediction.
Radiation Reaction from Soft Theorems
Authors: Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano
Preprint number: UUITP-03/21
Abstract: Radiation reaction (RR) terms at the third post-Minkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the non-relativistic, relativistic, and ultra-relativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which short-circuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PM-order connection that we apply, in particular, to Einstein's gravity and to its Jordan-Brans-Dicke extension. In the former case we find full agreement with a recent result by Damour obtained through a very different reasoning.
Cosmic eggs to relax the cosmological constant
Authors: Thomas Hertog, Rob Tielemans, Thomas van Riet
Preprint number: UUITP-02/21
Abstract: In theories with extra dimensions, the cosmological hierarchy problem can be thought of as the unnaturally large radius of the observable universe in Kaluza-Klein units. We sketch a dynamical mechanism that relaxes this. In the early universe scenario we propose, three large spatial dimensions arise through tunneling from a 'cosmic egg', an effectively one-dimensional configuration with all spatial dimensions compact and of comparable, small size. If the string landscape is dominated by low-dimensional compactifications, cosmic eggs would be natural initial conditions for cosmology. A quantum cosmological treatment of a toy model egg predicts that, in a variant of the Hartle-Hawking state, cosmic eggs break to form higher dimensional universes with a small, but positive cosmological constant or quintessence energy. Hence cosmic egg cosmology yields a scenario in which the seemingly unnaturally small observed value of the vacuum energy can arise from natural initial conditions.
Inozemtsev system as Seiberg-Witten integrable system
Authors: Philip Argyres, Oleg Chalykh, Yongchao Lu
Preprint number: UUITP-01/21
Abstract: In this work we establish that the Inozemtsev system is the Seiberg-Witten integrable system encoding the Coulomb branch physics of 4d \cN=2 USp(2N) gauge theory with four fundamental and (for N≥2) one antisymmetric tensor hypermultiplets. We describe the transformation from the spectral curves and canonical one-form of the Inozemtsev system in the N=1 and N=2 cases to the Seiberg-Witten curves and differentials explicitly, along with the explicit matching of the modulus of the elliptic curve of spectral parameters to the gauge coupling of the field theory, and of the couplings of the Inozemtsev system to the field theory mass parameters. This result is a particular instance of a more general correspondence between crystallographic elliptic Calogero-Moser systems with Seiberg-Witten integrable systems, which will be explored in future work.