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Register a new userSpectrum of local boundary operators from boundary form factor bootstrap
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Using the recently introduced boundary form factor bootstrap equations, we map the complete space of their solutions for the boundary version of the scaling Lee-Yang model and sinh-Gordon theory. We show that the complete space of solutions, graded by the ultraviolet behaviour of the form factors can be brought into correspondence with the spectrum of local boundary operators expected from boundary conformal field theory, which is a major evidence for the correctness of the boundary form factor bootstrap framework.
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Boundary form factor axioms are derived for the matrix elements of local boundary operators in integrable 1+1 dimensional boundary quantum field theories using the analyticity properties of correlators via the boundary reduction formula. Minimal solutions are determined for the integrable boundary perturbations of the free boson, free fermion (Ising), Lee-Yang and sinh-Gordon models and the two point functions calculated from them are checked against the exact solutions in the free cases and against the conformal data in the ultraviolet limit for the Lee-Yang model. In the case of the free boson/fermion the dimension of the solution space of the boundary form factor equation is shown to match the number of independent local operators. We obtain excellent agreement which proves not only the correctness of the solutions but also confirms the form factor axioms.
We study breaking and restoration of supersymmetry in five-dimensional theories by determining the mass spectrum of fermions from their equations of motion. Boundary conditions can be obtained from either the action principle by extremizing an appropriate boundary action (interval approach) or by assigning parities to the fields (orbifold approach). In the former, fields extend continuously from the bulk to the boundaries, while in the latter the presence of brane mass-terms cause fields to jump when one moves across the branes. We compare the two approaches and in particular we carefully compute the non-trivial jump profiles of the wavefunctions in the orbifold picture for very general brane mass terms. We also include the effect of the Scherk-Schwarz mechanism in either approach and point out that for a suitable tuning of the boundary actions supersymmetry is present for arbitrary values of the Scherk-Schwarz parameter. As an application of the interval formalism we construct bulk and boundary actions for super Yang-Mills theory. Finally we extend our results to the warped Randall-Sundrum background.
In this paper, we apply the form factor bootstrap approach to branch point twist fields in the $q$-state Potts model for $qleq 3$. For $q=3$ this is an integrable interacting quantum field theory with an internal discrete $mathbb{Z}_3$ symmetry and therefore provides an ideal starting point for the investigation of the symmetry resolved entanglement entropies. However, more generally, for $qleq 3$ the standard Renyi and entanglement entropies are also accessible through the bootstrap programme. In our work we present form factor solutions both for the standard branch point twist field with $qleq 3$ and for the composite (or symmetry resolved) branch point twist field with $q=3$. In both cases, the form factor equations are solved for two particles and the solutions are carefully checked via the $Delta$-sum rule. Using our analytic predictions, we compute the leading finite-size corrections to the entanglement entropy and entanglement equipartition for a single interval in the ground state.
We introduce a -- somewhat holographic -- dictionary between gravitational observables for scattering processes (measured at the boundary) and adiabatic invariants for bound orbits (in the bulk), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the two-body problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic orbits (such as the periastron advance $DeltaPhi$) through analytic continuation, via a radial action depending only on boundary data. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, $Omega(E)$, directly from scattering information. As an example, using the results in Bern et al. [1901.04424, 1908.01493], we readily derive $Omega(E)$ and $DeltaPhi(J,E)$ to two-loop orders. We also provide closed-form expressions for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We then perform a partial PM resummation, using a no-recoil approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy.
Boundary states for D-branes at orbifold fixed points are constructed in close analogy with Cardys derivation of consistent boundary states in RCFT. Comments are made on the interpretation of the various coefficients in the explicit expressions, and the relation between fractional branes and wrapped branes is investigated for $mathbb{C}^2/Gamma$ orbifolds. The boundary states are generalised to theories with discrete torsion and a new check is performed on the relation between discrete torsion phases and projective representations.
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