We propose using smeared boundary states $e^{-\tau H}|\cal B\rangle$ as
variational approximations to the ground state of a conformal field theory
deformed by relevant bulk operators. This is motivated by recent studies of
quantum quenches in CFTs and of the entanglement spectrum in massive theories.
It gives a simple criterion for choosing which boundary state should correspond
to which combination of bulk operators, and leads to a rudimentary phase
diagram of the theory in the vicinity of the RG fixed point corresponding to
the CFT, as well as rigorous upper bounds on the universal amplitude of the
free energy. In the case of the 2d minimal models explicit formulae are
available. As a side result we show that the matrix elements of bulk operators
between smeared Ishibashi states are simply given by the fusion rules of the
CFT.Comment: 17 pages, 3 figures. v3: Reference to related work added; analysis of
  minimal models clarified; reformatted to conform with SciPost submission
  guidelines. v4: discussion of tricritical Ising expanded; minor improvements
  and added references suggested by referee

Cardy, John

English

arXiv

We propose using smeared boundary states
e^{-\tau H}|\cal B\rangle
as variational approximations to the ground state of a conformal field
theory deformed by relevant bulk operators. This is motivated by recent
studies of quantum quenches in CFTs and of the entanglement spectrum in
massive theories. It gives a simple criterion for choosing which
boundary state should correspond to which combination of bulk operators,
and leads to a rudimentary phase diagram of the theory in the vicinity
of the RG fixed point corresponding to the CFT, as well as rigorous
upper bounds on the universal amplitude of the free energy. In the case
of the 2d minimal models explicit formulae are available. As a side
result we show that the matrix elements of bulk operators between
smeared Ishibashi states are simply given by the fusion rules of the
CFT.</jats:p

John Cardy

Crossref

SciPost Physics

Bulk Renormalization Group Flows and Boundary States in Conformal Field  Theories

We propose using smeared boundary states $e^{-\tau H}|\cal B\rangle$ as

variational approximations to the ground state of a conformal field theory

deformed by relevant bulk operators. This is motivated by recent studies of

quantum quenches in CFTs and of the entanglement spectrum in massive theories.

It gives a simple criterion for choosing which boundary state should correspond

to which combination of bulk operators, and leads to a rudimentary phase

diagram of the theory in the vicinity of the RG fixed point corresponding to

the CFT, as well as rigorous upper bounds on the universal amplitude of the

free energy. In the case of the 2d minimal models explicit formulae are

available. As a side result we show that the matrix elements of bulk operators

between smeared Ishibashi states are simply given by the fusion rules of the

CFT

Bulk Renormalization Group Flows and Boundary States in Conformal Field Theories

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