A bstract A state in a quantum system with a given global symmetry, G , can be sensitive to the presence of boundaries, which may either preserve or break this symmetry. In this work, we investigate how conformal invariant boundary conditions influence the G -symmetry breaking through the lens of the entanglement asymmetry, a quantifier of the “distance” between a symmetry-broken state and its symmetrized counterpart. By leveraging 2D boundary conformal field theory (BCFT), we investigate the symmetry breaking for both finite and compact Lie groups. Beyond the leading order term, we also compute the subleading corrections in the subsystem size, highlighting their dependence on the symmetry group G and the BCFT operator content. We further explore the entanglement asymmetry following a global quantum quench, where a symmetry-broken state evolves under a symmetry-restoring Hamiltonian. In this dynamical setting, we compute the entanglement asymmetry by extending the method of images to a BCFT with non-local objects such as invertible symmetry defects.A bstract A state in a quantum system with a given global symmetry, G , can be sensitive to the presence of boundaries, which may either preserve or break this symmetry. In this work, we investigate how conformal invariant boundary conditions influence the G -symmetry breaking through the lens of the entanglement asymmetry, a quantifier of the “distance” between a symmetry-broken state and its symmetrized counterpart. By leveraging 2D boundary conformal field theory (BCFT), we investigate the symmetry breaking for both finite and compact Lie groups. Beyond the leading order term, we also compute the subleading corrections in the subsystem size, highlighting their dependence on the symmetry group G and the BCFT operator content. We further explore the entanglement asymmetry following a global quantum quench, where a symmetry-broken state evolves under a symmetry-restoring Hamiltonian. In this dynamical setting, we compute the entanglement asymmetry by extending the method of images to a BCFT with non-local objects such as invertible symmetry defects.

arXiv:2411.09792Journal of High Energy PhysicsJan 9, 202519 citations

Breaking Symmetries: $\mathcal{N} = 2$ Spin Chains and Conformal Field Theory at Finite TemperatureBreaking Symmetries: $\mathcal{N} = 2$ Spin Chains and Conformal Field Theory at Finite Temperature

Deniz N. Bozkurt

Conformal field theories (CFTs) and supersymmetric field theories constitute special classes of quantum field theories with applications ranging from critical phenomena and confinement to quantum gravity via holography. Their large symmetry groups make them ideal testing grounds for theoretical developments, enabling the use of powerful and elegant methods. Among these, conformal bootstrap and integrability have proven particularly successful. In this thesis, we take steps toward extending these methods beyond their conventional domains by breaking conformal symmetry through finite temperature effects and reducing supersymmetry via orbifolding. For spin chains arising from $\mathcal{N} = 2$ superconformal field theories obtained by orbifolding $\mathcal{N} = 4$ super Yang–Mills theory in four dimensions, we generalize the coordinate Bethe ansatz by incorporating long-range corrections.On the conformal bootstrap side, after breaking conformality by placing the CFT on a d-dimensional cylinder, we develop an analytic framework based on dispersion relations. We apply this method to several theories, including large-N CFTs in four dimensions. Furthermore, we combine this analytic approach with existing numerical bootstrap techniques at finite temperature to compute new thermal correlation functions in the three-dimensional Ising CFT.Conformal field theories (CFTs) and supersymmetric field theories constitute special classes of quantum field theories with applications ranging from critical phenomena and confinement to quantum gravity via holography. Their large symmetry groups make them ideal testing grounds for theoretical developments, enabling the use of powerful and elegant methods. Among these, conformal bootstrap and integrability have proven particularly successful. In this thesis, we take steps toward extending these methods beyond their conventional domains by breaking conformal symmetry through finite temperature effects and reducing supersymmetry via orbifolding. For spin chains arising from $\mathcal{N} = 2$ superconformal field theories obtained by orbifolding $\mathcal{N} = 4$ super Yang–Mills theory in four dimensions, we generalize the coordinate Bethe ansatz by incorporating long-range corrections.On the conformal bootstrap side, after breaking conformality by placing the CFT on a d-dimensional cylinder, we develop an analytic framework based on dispersion relations. We apply this method to several theories, including large-N CFTs in four dimensions. Furthermore, we combine this analytic approach with existing numerical bootstrap techniques at finite temperature to compute new thermal correlation functions in the three-dimensional Ising CFT.

Sep 16, 20260 citations

Quantum group approach to conformal field theory

Luis Álvarez-Gaumé

Nuclear Physics B - Proceedings SupplementsAug 1, 19901 citation

Modular Hamiltonian for Excited States in Conformal Field Theory

Nima Lashkari

We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.

arXiv:1508.03506Physical Review LettersJul 21, 201683 citations

Breaking Symmetries:

\mathcal{N} = 2

Spin Chains and Conformal Field Theory at Finite Temperature

\mathcal{N} = 2

superconformal field theories obtained by orbifolding

\mathcal{N} = 4

super Yang–Mills theory in four dimensions, we generalize the coordinate Bethe ansatz by incorporating long-range corrections.On the conformal bootstrap side, after breaking conformality by placing the CFT on a d-dimensional cylinder, we develop an analytic framework based on dispersion relations. We apply this method to several theories, including large-N CFTs in four dimensions. Furthermore, we combine this analytic approach with existing numerical bootstrap techniques at finite temperature to compute new thermal correlation functions in the three-dimensional Ising CFT.