A cluster bootstrap for two-loop MHV amplitudes

We apply a bootstrap procedure to two-loop MHV amplitudes in planar N = 4 $$\mathcal{N}=4$$ super-Yang-Mills theory. We argue that the mathematically most complicated part (the Λ 2 B 2 coproduct component) of the n -particle amplitude is uniquely determined by a simple cluster algebra property together with a few physical constraints (dihedral symmetry, analytic structure, supersymmetry, and well-defined collinear limits). We present a concise, closed-form expression which manifests these properties for all n

Sub-sub-leading soft-graviton theorem in arbitrary dimension

The CHY formula which describes an n -point tree level scattering amplitude for scalars, gluons or gravitons in arbitrary dimension [22], is used to prove the sub-sub-leading soft-graviton theorem recently proposed by Cachazo and Strominger [13]

A note on soft factors for closed string scattering

In this note, it is shown that closed string graviton scattering amplitudes obey the same subleading soft limit as field theory graviton scattering amplitudes. The result is derived using a combination of recent results and methods including the subleading soft expansion for type I open string gluon disk scattering amplitudes, the single value projection for multiple ζ values, and the KLT relations in field and string theory

Subleading soft factor for string disk amplitudes

We investigate the behavior of superstring disk scattering amplitudes in the presence of a soft external momentum at finite string tension. We prove that there are no α ′-corrections to the field theory form of the subleading soft factor S (1) . At the end of this work, we also comment on the possibility to find the corresponding subleading soft factors in closed string theory using our result and the KLT relations

No unitary bootstrap for the fractal Ising model

We consider the conformal bootstrap for spacetime dimension 1 < d < 2. We determine bounds on operator dimensions and compare our results with various theoretical and numerical models, in particular with resummed ϵ -expansion and Monte Carlo simulations of the Ising model on fractal lattices. The bounds clearly rule out that these models correspond to unitary conformal field theories. We also clarify the d → 1 limit of the conformal bootstrap, showing that bounds can be — and indeed are — discontinuous in this limit. This discontinuity implies that for small ϵ = d − 1 the expected critical exponents for the Ising model are disallowed, and in particular those of the d − 1 expansion. Altogether these results strongly suggest that the Ising model universality class cannot be described by a unitary CFT below d = 2. We argue this also from a bootstrap perspective, by showing that the 2 ≤ d < 4 Ising “kink” splits into two features which grow apart below d = 2

Motivic amplitudes and cluster coordinates

In this paper we study motivic amplitudes — objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free from the ambiguities inherent in any attempt to choose particular functional representatives. We find that the cluster structure on the kinematic configuration space Conf n (ℙ 3 ) underlies the structure of motivic amplitudes. Specifically, we compute explicitly the coproduct of the two-loop seven-particle MHV motivic amplitude $\mathcal{A}_{7,2}^{\mathcal{M}}$ and find that like the previously known six-particle amplitude, it depends only on certain preferred coordinates known in the mathematics literature as cluster $\mathcal{X}$ - coordinates on Conf n (ℙ 3 ). We also find intriguing relations between motivic amplitudes and the geometry of generalized associahedrons, to which cluster coordinates have a natural combinatoric connection. For example, the obstruction to $\mathcal{A}_{7,2}^{\mathcal{M}}$ being expressible in terms of classica

Double soft theorems in gauge and string theories

We investigate the tree-level S-matrix in gauge theories and open superstring theory with several soft particles. We show that scattering amplitudes with two or three soft gluons of non-identical helicities behave universally in the limit, with multi-soft factors which are not the product of individual soft gluon factors. The results are obtained from the BCFW recursion relations in four dimensions, and further extended to arbitrary dimensions using the CHY formula. We also find new soft theorems for double soft limits of scalars and fermions in N = 4 $$\mathcal{N}=4$$ and pure N = 2 $$\mathcal{N}=2$$ SYM. Finally, we show that the double-soft-scalar theorems can be extended to open superstring theory without receiving any α ′ corrections

QED vacuum loops and inflation

A QED-based model of a new version of vacuum energy has recently been suggested, which leads to a simple, finite, one parameter representation of dark energy. An elementary, obvious, but perhaps radical generalization is then able to describe both dark energy and inflation in the same framework of vacuum energy. One further, obvious generalization then leads to a relation between inflation and the big bang, to the automatic inclusion of dark matter, and to a possible understanding of the birth (and death) of a universe

Bootstrapping the 3d Ising twist defect

Recent numerical results point to the existence of a conformally invariant twist defect in the critical 3d Ising model. In this note we show that this fact is supported by both epsilon expansion and conformal bootstrap calculations. We find that our results are in good agreement with the numerical data. We also make new predictions for operator dimensions and OPE coefficients from the bootstrap approach. In the process we derive universal bounds on one-dimensional conformal field theories and conformal line defects

Holography as a gauge phenomenon in Higher Spin duality

Employing the world line spinning particle picture. We discuss the appearance of several different ‘gauges’ which we use to gain a deeper explanation of the Collective/Gravity identification. We discuss transformations and algebraic equivalences between them. For a bulk identification we develop a ‘gauge independent’ representation where all gauge constraints are eliminated. This ‘gauge reduction’ of Higher Spin Gravity demonstrates that the physical content of 4D AdS HS theory is represented by the dynamics of an unconstrained scalar field in 6d. It is in this gauge reduced form that HS Theory can be seen to be equivalent to a 3 + 3 dimensional bi-local collective representation of CFT 3