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98,232
result(s) for
"Quantum Field Theories"
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The TT¯ deformation of quantum field theory as random geometry
A
bstract
We revisit the results of Zamolodchikov and others on the deformation of two-dimensional quantum field theory by the determinant det
T
of the stress tensor, commonly referred to as
T
T
¯
. Infinitesimally this is equivalent to a random coordinate transformation, with a local action which is, however, a total derivative and therefore gives a contribution only from boundaries or nontrivial topology. We discuss in detail the examples of a torus, a finite cylinder, a disk and a more general simply connected domain. In all cases the partition function evolves according to a linear diffusion-type equation, and the deformation may be viewed as a kind of random walk in moduli space. We also discuss possible generalizations to higher dimensions.
Journal Article
Circuit complexity in quantum field theory
A
bstract
Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a free scalar field theory for general dimensions. Applying the geometric approach of Nielsen to this quantum circuit model, the complexity of the state becomes the length of the shortest geodesic in the space of circuits. We compare the complexity of the ground state of the free scalar field to the analogous results from holographic complexity, and find some surprising similarities.
Journal Article
The S-matrix bootstrap. Part I: QFT in AdS
A
bstract
We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of the boundary correlators. We implement this strategy to obtain universal bounds on the strength of cubic couplings in 2D flat-space QFTs using 1D conformal bootstrap techniques. Our numerical results match precisely the analytic bounds obtained in our companion paper using S-matrix bootstrap techniques.
Journal Article
Circuit complexity in interacting QFTs and RG flows
A
bstract
We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the
ϕ
4
theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled ground state of the theory. Our approach uses Nielsen’s geometric method, which translates into working out the geodesic equation arising from a certain cost functional. We present a general method, making use of integral transforms, to do the required lattice sums analytically and give explicit expressions for the
d
= 2
,
3 cases. Our method enables a study of circuit complexity in the epsilon expansion for the Wilson-Fisher fixed point. We find that with increasing dimensionality the circuit depth increases in the presence of the
ϕ
4
interaction eventually causing the perturbative calculation to breakdown. We discuss how circuit complexity relates with the renormalization group.
Journal Article
The Analytic Wavefunction
A
bstract
The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic structure of wavefunction coefficients in Minkowski as a function of their kinematics. We introduce an
off-shell
wavefunction in terms of amputated time-ordered correlation functions and show that it is analytic in the complex energy plane except for possible singularities on the negative real axis. These singularities are determined to all loop orders by a simple energy-conservation condition. We confirm this picture by developing a Landau analysis of wavefunction loop integrals and corroborate our findings with several explicit calculations in scalar field theories. This analytic structure allows us to derive new UV/IR sum rules for the wavefunction that fix the coefficients in its low-energy expansion in terms of integrals of discontinuities in the corresponding UV-completion. In contrast to the analogous sum rules for scattering amplitudes, the wavefunction sum rules can also constrain total-derivative interactions. We explicitly verify these new relations at one-loop order in simple UV models of a light and a heavy scalar. Our results, which apply to both Lorentz invariant and boost-breaking theories, pave the way towards deriving wavefunction positivity bounds in flat and cosmological spacetimes.
Journal Article
The glueball spectrum of SU(3) gauge theory in 3 + 1 dimensions
A
bstract
We calculate the low-lying glueball spectrum of the SU(3) lattice gauge theory in 3 + 1 dimensions for the range
β ≤
6
.
50 using the standard plaquette action. We do so for states in all the representations
R
of the cubic rotation group, and for both values of parity
P
and charge conjugation
C
. We extrapolate these results to the continuum limit of the theory using the confining string tension
σ
as our energy scale. We also present our results in units of the
r
0 scale and, from that, in terms of physical ‘GeV’ units. For a number of these states we are able to identify their continuum spins
J
with very little ambiguity. We also calculate the topological charge
Q
of the lattice gauge fields so as to show that we have sufficient ergodicity throughout our range of
β
, and we calculate the multiplicative renormalisation of
Q
as a function of
β
. We also obtain the continuum limit of the SU(3) topological susceptibility.
Journal Article
Localized magnetic field in the O(N) model
A
bstract
We consider the critical
O
(
N
) model in the presence of an external magnetic field localized in space. This setup can potentially be realized in quantum simulators and in some liquid mixtures. The external field can be understood as a relevant perturbation of the trivial line defect, and thus triggers a defect Renormalization Group (RG) flow. In agreement with the
g
-theorem, the external localized field leads at long distances to a stable nontrivial defect CFT (DCFT) with
g <
1. We obtain several predictions for the corresponding DCFT data in the epsilon expansion and in the large
N
limit. The analysis of the large
N
limit involves a new saddle point and, remarkably, the study of fluctuations around it is enabled by recent progress in AdS loop diagrams. Our results are compatible with results from Monte Carlo simulations and we make several predictions that can be tested in the future.
Journal Article
Time evolution of complexity: a critique of three methods
A
bstract
In this work, we propose a testing procedure to distinguish between the different approaches for computing complexity. Our test does not require a direct comparison between the approaches and thus avoids the issue of choice of gates, basis, etc. The proposed testing procedure employs the information-theoretic measures Loschmidt echo and Fidelity; the idea is to investigate the sensitivity of the complexity (derived from the different approaches) to the evolution of states. We discover that only circuit complexity obtained directly from the wave function is sensitive to time evolution, leaving us to claim that it surpasses the other approaches. We also demonstrate that circuit complexity displays a universal behaviour — the complexity is proportional to the number of distinct Hamiltonian evolutions that act on a reference state. Due to this fact, for a given number of Hamiltonians, we can always find the combination of states that provides the maximum complexity; consequently, other combinations involving a smaller number of evolutions will have less than maximum complexity and, hence, will have resources. Finally, we explore the evolution of complexity in non-local theories; we demonstrate the growth of complexity is sustained over a longer period of time as compared to a local theory.
Journal Article
Defects in conformal field theory
A
bstract
We discuss consequences of the breaking of conformal symmetry by a flat or spherical extended operator. We adapt the embedding formalism to the study of correlation functions of symmetric traceless tensors in the presence of the defect. Two-point functions of a bulk and a defect primary are fixed by conformal invariance up to a set of OPE coefficients, and we identify the allowed tensor structures. A correlator of two bulk primaries depends on two cross-ratios, and we study its conformal block decomposition in the case of external scalars. The Casimir equation in the defect channel reduces to a hypergeometric equation, while the bulk channel blocks are recursively determined in the light-cone limit. In the special case of a defect of codimension two, we map the Casimir equation in the bulk channel to the one of a four-point function without defect. Finally, we analyze the contact terms of the stress-tensor with the extended operator, and we deduce constraints on the CFT data. In two dimensions, we relate the displacement operator, which appears among the contact terms, to the reflection coefficient of a conformal interface, and we find unitarity bounds for the latter.
Journal Article