Related papers: $p$-adic Mellin Amplitudes
For every prime number $p$ it is possible to define a $p$-adic version of the Veneziano amplitude and its higher-point generalizations. Multiplying together the real amplitude with all its $p$-adic counterparts yields the adelic amplitude.…
The computation of CFT correlation functions via Witten diagrams in AdS space can be simplified via the Mellin transform. Recently a set of Feynman rules for tree-level Mellin space amplitudes has been proposed for scalar theories. In this…
We explore a new way of probing scattering of closed strings in $AdS_5\times S^5$, which we call `the large $p$ limit'. It consists of studying four-point correlators of single-particle operators in $\mathcal{N}=4$ SYM at large $N$ and…
In the 2022 study, together with Paul McFadden and Kostas Skenderis, I analyzed tree-level 3- and 4-point Witten diagrams (amplitudes) of scalar operators in anti-de Sitter space in momentum space. This paper constitutes its extension to…
We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories (CFTs). This allows us to set up the non-perturbative Polyakov bootstrap for CFTs in Mellin…
We consider holographic CFTs and study their large $N$ expansion. We use Polyakov-Mellin bootstrap to extract the CFT data of all operators, including scalars, till $O(1/N^4)$. We add a contact term in Mellin space, which corresponds to an…
In this work we present a closed form expression for Polyakov blocks in Mellin space for arbitrary spin and scaling dimensions. We provide a prescription to fix the contact term ambiguity uniquely by reducing the problem to that of fixing…
Using the theory of $(\phi,\Gamma)$-modules and the formalism of Selmer complexes we construct the p-adic height for p-adic representations with coefficients in an affinoid algebra over $Q_p$.
The scalar field exchange diagram for the correlation function of four scalar operators is evaluated in anti-de Sitter space, $AdS_{d+1}$. The conformal dimensions $\Delta_i$, $i=1,...,4$ of the scalar operators and the dimension $\Delta$…
We compute the disk amplitude of three closed strings in the pure spinor formalism. Among others, this amplitude probes tree-level gravitational interactions in the presence of Dp-branes. After disentangling holomorphic and anti-holomorphic…
Amplitudes $A_n$ in $d$-dimensional scalar field theory are generated, to all orders in the coupling constant and at $n$-point. The amplitudes are expressed as a series in the mass $m$ and coupling $\lambda$. The inputs are the classical…
We further develop celestial Mellin amplitudes arXiv:2412.11992 to capture the exchange of particles with spin. For massless external scalar fields, we derive closed-form celestial Mellin amplitudes for a spin-1 and spin-2…
In these proceedings, we discuss the recent approach of Ref. [1] for the construction of compact Ans\"atze for scattering amplitudes. The method builds powerful constraints on the analytic structure of the rational functions in amplitudes…
We present a rewiew and also new possible applications of $p$-adic numbers to pre-spacetime physics. It is shown that instead of the extension $R^n\to Q_p^n$, which is usually implied in $p$-adic quantum field theory, it is possible to…
We give a criterion of the semisimplicity of a p-adic unitary representation of a topological monoid by the reduction of the associated operator algebra.
We present a new p-adic version of the Jackiw-Rebbi model. In the new model, the real numeric line is replaced by a p-adic line (the field of p-adic numbers Q_{p}), and the Dirac Hamiltonian is replaced by a non-local operator acting on…
The biadjoint scalar partial amplitude, $m_n(\mathbb{I},\mathbb{I})$, can be expressed as a single integral over the positive tropical Grassmannian thus producing a Global Schwinger Parameterization. The first result in this work is an…
We study the thermodynamic formalism associated with the Schneider map on the p-adic integers $p\mathbb{Z}_p$ . By introducing a geometric potential that captures the expansion of cylinder sets generated by the map, we define a Lyapunov…
Celestial amplitudes, obtained by applying Mellin transform and analytic continuation on "ordinary" amplitudes, have interesting properties which may provide useful insights on the underlying theory. Their analytic structures are thus of…
We give a construction of a wide class of modular symbols attached to reductive groups. As an application we construct a p-adic distribution interpolating the special values of the twisted Rankin-Selberg L-function attached to cuspidal…