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Register a new userDefect scaling Lee-Yang model from the perturbed DCFT point of view
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We analyze the defect scaling Lee-Yang model from the perturbed defect conformal field theory (DCFT) point of view. First the defect Lee-Yang model is solved by calculating its structure constants from the sewing relations. Integrable defect perturbations are identified in conformal defect perturbation theory. Then pure defect flows connecting integrable conformal defects are described. We develop a defect truncated conformal space approach (DTCSA) to analyze the one parameter family of integrable massive perturbations in finite volume numerically. Fusing the integrable defect to an integrable boundary the relation between the IR and UV parameters can be derived from the boundary relations. We checked these results by comparing the spectrum for large volumes to the scattering theory.
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The supersymmetric Lee-Yang model is arguably the simplest interacting supersymmetric field theory in two dimensions, albeit non-unitary. A natural question is if there is an analogue of supersymmetric Lee-Yang fixed point in higher dimensions. The absence of any $mathbb{Z}_2$ symmetry (except for fermion numbers) makes it impossible to approach it by using perturbative $epsilon$ expansions. We find that the truncated conformal bootstrap suggests that candidate fixed points obtained by the dimensional continuation from two dimensions annihilate below three dimensions, implying that there is no supersymmetric Lee-Yang fixed point in three dimensions. We conjecture that the corresponding phase transition, if any, will be the first order transition.
The four dimensional $mathcal{N}=4$ super-Yang-Mills (SYM) theory exhibits rich dynamics in the presence of codimension-one conformal defects. The new structure constants of the extended operator algebra consist of one-point functions of local operators which are nonvanishing due to the defect insertion and carry nontrivial coupling dependence. We study an important class of half-BPS superconformal defects engineered by D5 branes that share three common directions with the D3 branes and involve Nahm pole configurations for the SYM fields on the D3 brane worldvolume. In the planar large $N$ limit, we obtain non-perturbative results in the t Hooft coupling $lambda$ for the defect one-point functions of both BPS and non-BPS operators, building upon recent progress in localization and integrability methods. For BPS operator insertions in the SYM with D5-brane type boundary or interface, we derive an effective two dimensional defect-Yang-Mills (dYM) theory from supersymmetric localization, which gives an efficient way to extract defect observables and generates a novel matrix model for the defect one-point function. By solving the matrix model in the large $N$ limit, we obtain exact results in $lambda$ which interpolate between perturbative Feynman diagram contributions in the weak coupling limit and IIB string theory predictions on $AdS_5times S^5$ in the strong coupling regime, providing a precision test of AdS/CFT with interface defects. For general non-BPS operators, we develop a non-perturbative bootstrap-type program for integrable boundary states on the worldsheet of the IIB string theory, corresponding to the interface defects in the planar SYM. Such integrable boundary states are constrained by a set of general consistency conditions for which we present explicit solutions that reproduce and extend the known results at weak coupling from integrable spin-chain methods.
In this paper we study the ultraviolet and infrared behaviour of the self energy of a point-like charge in the vector and scalar Lee-Wick electrodynamics in a $d+1$ dimensional space time. It is shown that in the vector case, the self energy is strictly ultraviolet finite up to $d=3$ spatial dimensions, finite in the renormalized sense for any $d$ odd, infrared divergent for $d=2$ and ultraviolet divergent for $d>2$ even. On the other hand, in the scalar case, the self energy is striclty finite for $dleq 3$, and finite, in the renormalized sense, for any $d$ odd.
We study tree level one-point functions of non-protected scalar operators in the defect CFT, based on N=4 SYM, which is dual to the SO(5) symmetric D3-D7 probe brane system with non-vanishing instanton number. Whereas symmetries prevent operators from the SU(2) and SU(3) sub-sectors from having non-vanishing one-point functions, more general scalar conformal operators, which in particular constitute Bethe eigenstates of the integrable SO(6) spin chain, are allowed to have non-trivial one-point functions. For a series of operators with a small number of excitations we find closed expressions in terms of Bethe roots for these one-point functions, valid for any value of the instanton number. In addition, we present some numerical results for operators with more excitations.
Lee-Yang zeros are points on the complex plane of magnetic field where the partition function of a spin system is zero and therefore the free energy diverges. Lee-Yang zeros and their generalizations are ubiquitous in many-body systems and they fully characterize the analytic properties of the free energy and hence thermodynamics of the systems. Determining the Lee-Yang zeros is not only fundamentally important for conceptual completeness of thermodynamics and statistical physics but also technically useful for studying many-body systems. However, Lee-Yang zeros have never been observed in experiments, due to the intrinsic difficulty that Lee-Yang zeros would occur only at complex values of magnetic field, which are unphysical. Here we report the first observation of Lee-Yang zeros, by measuring quantum coherence of a probe spin coupled to an Ising-type spin bath. As recently proposed, the quantum evolution of the probe spin introduces a complex phase factor, and therefore effectively realizes an imaginary magnetic field on the bath. From the measured Lee-Yang zeros, we reconstructed the free energy of the spin bath and determined its phase transition temperature. This experiment demonstrates quantum coherence probe as a useful approach to studying thermodynamics in the complex plane, which may reveal a broad range of new phenomena that would otherwise be inaccessible if physical parameters are restricted to be real numbers.
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