Worldsheet Geometries of Ambitwistor String

Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.Comment: 31 pages, publised versio

Open superstring field theory based on the supermoduli space

We present a new approach to formulating open superstring field theory based on the covering of the supermoduli space of super-Riemann surfaces and explicitly construct a gauge-invariant action in the Neveu-Schwarz sector up to quartic interactions. The cubic interaction takes a form of an integral over an odd modulus of disks with three punctures and the associated ghost is inserted. The quartic interaction takes a form of an integral over one even modulus and two odd moduli, and it can be interpreted as the integral over the region of the supermoduli space of disks with four punctures which is not covered by Feynman diagrams with two cubic vertices and one propagator. As our approach is based on the covering of the supermoduli space, the resulting theory naturally realizes an $A_\infty$ structure, and the two-string product and the three-string product used in defining the cubic and quartic interactions are constructed to satisfy the $A_\infty$ relations to this order.Comment: 60 pages, 3 figures; v2: minor corrections and references added; v3: a proof that the quartic vertex is unambiguously defined for general off-shell states added in appendix A.5, version published in JHE

5d/6d DE instantons from trivalent gluing of web diagrams

We propose a new prescription for computing the Nekrasov partition functions of five-dimensional theories with eight supercharges realized by gauging non-perturbative flavor symmetries of three five-dimensional superconformal field theories. The topological vertex formalism gives a way to compute the partition functions of the matter theories with flavor instanton backgrounds, and the gauging is achieved by summing over Young diagrams. We apply the prescription to calculate the Nekrasov partition functions of various five-dimensional gauge theories such as $\mathrm{SO}(2N)$ gauge theories with or without hypermultiplets in the vector representation and also pure $E_6, E_7, E_8$ gauge theories. Furthermore, the technique can be applied to computations of the Nekrasov partition functions of five-dimensional theories which arise from circle compactifications of six-dimensional minimal superconformal field theories characterized by the gauge groups $\mathrm{SU}(3), \mathrm{SO}(8), E_6, E_7, E_8$. We exemplify our method by comparing some of the obtained partition functions with known results and find perfect agreement. We also present a prescription of extending the gluing rule to the refined topological vertex.Comment: 66 pages, 28 figures; v2: typos corrected, references added and a Mathematica notebook for some checks adde

Anomaly polynomial of E-string theories

We determine the anomaly polynomial of the E-string theory and its higher-rank generalizations, that is, the 6d $\mathcal{N} =(1, 0)$ superconformal theories on the worldvolume of one or multiple M5-branes embedded within the end-of-the-world brane with $E_8$ symmetry.Comment: v2: 16 pages; typos correcte

Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae

't Hooft anomalies are known to induce specific contributions to the effective action at finite temperature. We present a general method to directly calculate such contributions from the anomaly polynomial of a given theory, including a term which involves a $U(1)$ connection for the thermal circle isometry. Based on this observation, we show that the asymptotic behavior of the superconformal index of $4d$ $\mathcal{N}=1$ theories on the "second sheet" can be calculated by integrating the anomaly polynomial on a particular background. The integration is then performed by an equivariant method to reproduce known results. Our method only depends on the anomaly polynomial and therefore the result is applicable to theories without known Lagrangian formulation. We also present a new formula that relates the behavior of $6d$ $\mathcal{N}=(1,0)$ SCFTs on the second sheet to the anomaly polynomial.Comment: 34 pages; v2: minor edits, added references and comment