Spectroscopy instead of scattering: particle experimentation in AdS spacetime

Abstract

Particle experiments are difficult at weak coupling because interactions are rare and a huge number of collision attempts are needed to attain significant precision. One often hears that 'one Higgs boson is produced in a billion of collisions at LHC.' In this essay, we fantasize about possible advantages afforded in this regard by performing experiments in anti-de Sitter (AdS) spacetime instead of a usual collider in a nearly-flat spacetime. Being a perfectly resonant cavity, the AdS spacetime enhances all nonlinear interactions, which therefore produce effects of order one no matter how small the couplings are, provided that one waits long enough. These effects are encoded in spectroscopic data, namely, the fine splittings of the energy levels which would have been highly degenerate in AdS if no interactions were present. Over long times, such energy shifts let different components of wavefunctions drift completely out-of-phase, producing large effects for arbitrarily small interactions.

Energy-level splitting for weakly interacting bosons in a harmonic trap

“…We note in passing that the structure of the unperturbed levels, and the diagonalization problem arising here at linear order in g, parallel closely what one would have encountered if treating quantum relativistic interacting fields in Anti-de Sitter spacetime (a brief summary can be found in [21]). This is not a coincidence, since nonrelativistic bosonic fields in harmonic potentials arise systematically through taking nonrelativistic limits of field systems in Antide Sitter spacetime [22,23].…”

“…Thus, any block with E = M is entirely composed of LLL states. Creation-annihilation operators corresponding to non-LLL modes do not contribute to matrix elements (21) between any two states in an E = M block. We shall refer to the E = M blocks as 'LLL blocks' for obvious reasons.…”

“…Because the energy carried by |{η} and |{η } in (21) is the same, the two annihilation operators in H int must remove the same total amount of energy as what the two creation operators add, i.e., only terms with n 1 + n 2 = n 3 + n 4 in (18) may contribute in the matrix elements (21). This results in a simplification that is straightforward, but has welcome analytic consequences.…”

Bounds on quantum evolution complexity via lattice cryptography

“…In contrast to the rich array of classical dynamical behaviors, the corresponding quantum theory is very economical in its structure and can be explored via an operation as simple as diagonalizing finite-sized numerical matrices [37]. (We mention in addition that (1.1) arises directly in the process of applying the standard Hamiltonian perturbation theory for the degenerate spectrum of quantum fields in strongly resonant domains at first order in the quartic interaction strength [69][70][71][72]. )…”

Time-periodicities in holographic CFTs

“…We shall explain, following [26], that similar patterns should be expected in maximally rotating sectors of gravitating systems, but re-covering them explicitly would require substantial technical work beyond the scope of our treatment. As outlined already in [34], the problem of finding these energy shifts can be reduced to diagonalizing a specific quantum resonant system [35], whose Hamiltonian is a quartic combination of creation-annihilation operators. Such quantum resonant systems are, on the one hand, related to bosonic embedded Gaussian ensembles of random matrix theory [36], albeit without randomness in the couplings, and on the other hand, can be seen as a bosonic analog of the SYK model [37][38][39] that has attracted much attention in the context of gravitational holography.…”