Preprints 2024

Super YangMills on Branched Covers and Weighted Projective Spaces
Authors: Roman Mauch and Lorenzo Ruggeri
Preprint number: UUITP10/24
Abstract: In this work we conjecture the Coulomb branch partition function, including
flux and instanton contributions, for the N = 2 vector multiplet on weighted projective
space CP2N for equivariant DonaldsonWitten and “Pestunlike” theories. More precisely,
we claim that this partition function agrees with the one computed on a certain branched
cover of CP2 upon matching conical deficit angles with corresponding branch indices. Our
conjecture is substantiated by checking that similar partition functions on spindles agree
with their equivalent on certain branched covers of CP1. We compute the oneloop deter
minant on the branched cover of CP2 for all flux sectors via dimensional reduction from
the N = 1 vector multiplet on a branched fivesphere along a free S1action. Our work
paves the way for obtaining partition functions on more generic symplectic toric orbifolds. 
Nonholomorphic modular forms from zeta generators
Authors: Daniele Dorigoni, Mehregan Doroudiani, Joshua Drewitt, Martijn Hidding, Axel Kleinschmidt, Oliver Schlotterer, Leila Schneps and Bram Verbeek
Preprint number: UUITP09/24
Abstract: We study nonholomorphic modular forms built from iterated integrals of holomorphic modular forms for $\SLtwoZ$ known as equivariant iterated Eisenstein integrals. A special subclass of them furnishes an equivalent description of the modular graph forms appearing in the lowenergy expansion of string amplitudes at genus one. Notably the Fourier expansion of modular graph forms contains singlevalued multiple zeta values. We deduce the appearance of products and higherdepth instances of multiple zeta values in equivariant iterated Eisenstein integrals, and ultimately modular graph forms, from the coefficients of simpler odd Riemann zeta values. This analysis relies on socalled zeta generators which act on certain noncommutative variables in the generating series of the iterated integrals. From an extension of these noncommutative variables we incorporate iterated integrals involving holomorphic cusp forms into our setup and use them to construct the modular completion of triple Eisenstein integrals. Our work represents a fully explicit realisation of the modular graph forms within Brown's framework of equivariant iterated Eisenstein integrals and reveals structural analogies between singlevalued period functions appearing in genus zero and one string amplitudes. 
Effective interactions of the open bosonic string via field theory
Authors: Lucia M. Garozzo, Alfredo Guevara
Preprint number: UUITP08/24
Abstract: We describe a method to extract an effective Lagrangian description for open bosonic strings, at zero transcendentality. The method relies on a particular formulation of its scattering amplitudes derived from colorkinematics duality. More precisely, starting from a (DF)^2 + YM quantum field theory, we integrate out all the massive degrees of freedom to generate an expansion in the inverse string tension α′. We explicitly compute the Lagrangian terms through O(α′^4), and target the sector of operators proportional to F^4 to all orders in α′.

Tduality between 6d (2,0) and (1,1) Little String Theories with Twist
Authors: HeeCheol Kim, Kimyeong Lee, Kaiwen Sun, Xin Wang
Preprint number: UUITP07/24

On Intermediate Exceptional Series
Authors: Kimyeong Lee, Kaiwen Sun, Haowu Wang
Preprint number: UUITP06/24
Abstract: The FreudenthalTits magic square m(A_{1},A_{2}) for A=R,C,H,O of semisimple Lie algebras can be extended by including the sextonions S. A series of nonreductive Lie algebras naturally appear in the new row associated with the sextonions, which we will call the intermediate exceptional series, with the largest one as the intermediate Lie algebra E_{7+1/2} constructed by LandsbergManivel. We study various aspects of the intermediate vertex operator (super)algebras associated with the intermediate exceptional series, including rationality, coset constructions, irreducible modules, (super)characters and modular linear differential equations. For all g_{I} belonging to the intermediate exceptional series, the intermediate VOA L_{1}(g_{I}) has characters of irreducible modules coinciding with those of the simple rational C_{2}cofinite Walgebra W_{h∨/6}(g,f_{θ}) studied by Kawasetsu, with g belonging to the CvitanovićDeligne exceptional series. We propose some new intermediate VOA L_{k}(g_{I}) with integer level k and investigate their properties. For example, for the intermediate Lie algebra D_{6+1/2} between D_{6}and E_{7} in the subexceptional series and also in Vogel's projective plane, we find that the intermediate VOA L_{2}(D_{6+1/2}) has a simple current extension to a SVOA with four irreducible NeveuSchwarz modules. We also provide some (super) coset constructions such as L_{2}(E_{7})/L_{2}(D_{6+1/2}) and L_{1}(D_{6+1/2})^{⊗2}\!/L_{2}(D_{6+1/2}). In the end, we find that the theta blocks associated with the intermediate exceptional series produce some new holomorphic Jacobi forms of critical weight and lattice index.

N=(2,2) superfields and geometry revisited
Authors: Chris Hull and Maxim Zabzine
Preprint number: UUITP05/24

Charges and topology in linearised gravity
Authors: Chris Hull, Maxwell L. Hutt and Ulf Lindström
Preprint number: UUITP04/24
Abstract: Covariant conserved 2form currents for linearised gravity are constructed by contracting the linearised curvature with conformal KillingYano tensors. The corre sponding conserved charges were originally introduced by Penrose and have recently been interpreted as the generators of generalised symmetries of the graviton. We introduce an offshell refinement of these charges and find the relation between these improved Penrose charges and the linearised version of the ADM momentum and angular momentum. If the graviton field is globally welldefined on a background Minkowski space then some of the Penrose charges give the momentum and angular momentum while the remainder vanish. We consider the generalisation in which the graviton has Dirac string singularities or is defined locally in patches, in which case the conventional ADM expressions are not invariant under the graviton gauge symmetry in general. We modify these expressions to render them gaugeinvariant and show that the Penrose charges give these modified charges plus certain magnetic gravitational charges. We discuss properties of the Penrose charges, generalise to toroidal KaluzaKlein compactifications and check our results in a number of examples.

The soaring kite: a tale of two punctured tori
Authors: Mathieu Giroux, Andrzej Pokraka, Franziska Porkert, Yoann Sohnle
Preprint number: UUITP03/24
Abstract: We consider the 5mass kite family of Feynman integrals and present a systematic approach for constructing an εform basis, along with its differential equation pulled back onto the moduli space of two tori. Each torus is associated with one of the two distinct elliptic curves this family depends on. We demonstrate how the relevant punctures, which are required to parametrize the full image of the kinematic space onto this moduli space, can be obtained from integrals over maximal cuts. Given an appropriate boundary value, the differential equation is systematically solved in terms of iterated integrals over KroneckerEisenstein gkernels and modular forms. Then, the numerical evaluation of the master integrals is discussed, and important challenges in that regard are emphasized. In an appendix, we introduce new relations between gkernels.

What can abelian gauge theories teach us about kinematic algebras?
Authors: Kymani ArmstrongWilliams, Silvia Nagy, Chris D. White, Sam Wikeley
Preprint number: UUITP–02/24
Abstract: The phenomenon of BCJ duality implies that gauge theories possess an abstract kinematic algebra, mirroring the nonabelian Lie algebra underlying the colour information. Although the nature of the kinematic algebra is known in certain cases, a full understanding is missing for arbitrary nonabelian gauge theories, such that one typically works outwards from wellknown examples. In this paper, we pursue an orthogonal approach, and argue that simpler abelian gauge theories can be used as a testing ground for clarifying our understanding of kinematic algebras. We first describe how classes of abelian gauge fields are associated with welldefined subgroups of the diffeomorphism algebra. By considering certain special subgroups, we show that one may construct interacting theories, whose kinematic algebras are inherited from those already appearing in a related abelian theory. Known properties of (anti)selfdual YangMills theory arise in this way, but so do new generalisations, including selfdual electromagnetism coupled to scalar matter. Furthermore, a recently obtained nonabelian generalisation of the NavierStokes equation fits into a similar scheme, as does ChernSimons theory. Our results provide useful input to further conceptual studies of kinematic algebras.

Plücker Coordinates and the Rosenfeld Planes
Authors: Jian Qiu
Preprint number: UUITP01/24
Abstract: The exceptional compact hermitian symmetric space EIII is the
quotient $E_6/SO(10)\times_{\mathbb{Z}_4}U(1)$.
We introduce the Plücker coordinates which give an embedding of EIII
into $\mathbb{C}P^{26}$ as a projective subvariety.
The subvariety is cut out by 27 Plücker relations.
We show that, using Clifford algebra, one can solve this over
determined system of relations, giving local coordinate charts to the
space. Our motivation is to understand EIII as the complex projective octonion
plane $(\mathbb{C}\otimes\mathbb{O})P^2$, which is a piece of folklore
scattered across literature. We will see that the EIII has an atlas whose transition functions have
clear octonion interpretations, apart from those covering a subvariety
of dimension 10 denoted $X_{\infty}$. This subvariety is itself a
hermitian symmetric space known as DIII, with no apparent octonion
interpretation. We give detailed analysis of the geometry in the
neighbourhood of $X_{\infty}$. We further decompose $X$ into $F_4$orbits: $X=Y_0\cup Y_{\infty}$, where $Y_0$ is an open $F_4$ orbit and is the complexified octonion
projective plane and $Y_{\infty}$ has codimension 1, and is needed to
complete $Y_0$ into a projective variety. This decomposition appears in
the classification of equivariant completion of homogeneous algebraic
varieties by Ahiezer \cite{Ahiezer}.