Twist Operators Research Articles

Quantum annealing with twisted fields

Quantum annealing (QA) is a promising method for solving combinational optimization problems and performing quantum chemical calculations. The main sources of errors in QA are the effects of decoherence and non-adiabatic transition. We propose a method for suppressing both these effects using inhomogeneous twist operators corresponding to the twist angles of transverse fields applied to qubits. Furthermore, we adopt variational methods to determine the optimal inhomogeneous twist operator for minimizing the energy of the state after QA. Our approach is useful for increasing the energy gap and/or making the quantum states robust against decoherence during QA. In summary, our results can pave the way to a new approach for realizing practical QA.

Entropy variations and light ray operators from replica defects

We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as n approaches 1 a contact term can emerge when the OPE contains defect operators of twist d − 2. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the n → 1 limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap. As a check, we show independently that in a large class of near vacuum states, the second variation of the entanglement entropy is given by a simple correlation function of averaged null energy operators as studied by Hofman and Maldacena. This suggests that sub-leading terms in the defect OPE are controlled by a defect version of the spin-3 non-local light ray operator and we speculate about the possible origin of such a defect operator. For free theories this contribution condenses to a contact term that leads to violations of QNEC saturation.

Generalized symmetries and Noether’s theorem in QFT

We show that generalized symmetries cannot be charged under a continuous global symmetry having a Noether current. Further, only non-compact generalized symmetries can be charged under a continuous global symmetry. These results follow from a finer classification of twist operators, which naturally extends to finite group global symmetries. They unravel topological obstructions to the strong version of Noether’s theorem in QFT, even if under general conditions a global symmetry can be implemented locally by twist operators (weak version). We use these results to rederive Weinberg-Witten’s theorem within local QFT, generalizing it to massless particles in arbitrary dimensions and representations of the Lorentz group. Several examples with local twists but without Noether currents are described. We end up discussing the conditions for the strong version to hold, dynamical aspects of QFT’s with non-compact generalized symmetries, scale vs conformal invariance in QFT, connections with the Coleman-Mandula theorem and aspects of global symmetries in quantum gravity.

Formula omitted]-operators and Nijenhuis operators of associative conformal algebras

We study O-operators of associative conformal algebras with respect to conformal bimodules. As natural generalizations of O-operators and dendriform conformal algebras, we introduce the notions of twisted Rota-Baxter operators and conformal NS-algebras. We show that twisted Rota-Baxter operators give rise to conformal NS-algebras, the same as O-operators induce dendriform conformal algebras. And we introduce a conformal analog of associative Nijenhuis operators and enumerate main properties. By using derived bracket construction of Kosmann-Schwarzbach and a method of Uchino, we obtain a graded Lie algebra whose Maurer-Cartan elements are given by O-operators. This allows us to construct cohomology of O-operators. This cohomology can be seen as the Hochschild cohomology of an associative conformal algebra with coefficients in a suitable conformal bimodule.

Universal Feature of Charged Entanglement Entropy.

Rényi entropies, S_{n}, admit a natural generalization in the presence of global symmetries. These "charged Rényi entropies" are functions of the chemical potential μ conjugate to the charge contained in the entangling region and reduce to the usual notions as μ→0. For n=1, this provides a notion of charged entanglement entropy. In this Letter, we prove that for a general d(≥3)-dimensional conformal field theory, the leading correction to the uncharged entanglement entropy across a spherical entangling surface is quadratic in the chemical potential, positive definite, and universally controlled (up to fixed d-dependent constants) by the coefficients C_{J} and a_{2}. These fully characterize, for a given theory, the current correlators ⟨JJ⟩ and ⟨TJJ⟩, as well as the energy flux measured at infinity produced by the insertion of the current operator. Our result is motivated by analytic holographic calculations for a special class of higher-curvature gravities coupled to a (d-2) form in general dimensions as well as for free fields in d=4. A proof for general theories and dimensions follows from previously known universal identities involving the magnetic response of twist operators introduced in A. Belin etal. [J. High Energy Phys. 12 (2013) 059.JHEPFG1029-847910.1007/JHEP12(2013)059] and basic thermodynamic relations.

Higher-derivative holography with a chemical potential

We carry out an extensive study of the holographic aspects of any-dimensional higher-derivative Einstein-Maxwell theories in a fully analytic and non-perturbative fashion. We achieve this by introducing the d-dimensional version of Electromagnetic Quasitopological gravities: higher-derivative theories of gravity and electromagnetism that propagate no additional degrees of freedom and that allow one to study charged black hole solutions analytically. These theories contain non-minimal couplings, that in the holographic context give rise to a modified 〈JJ〉 correlator as well as to a general 〈TJJ〉 structure whose coefficients we compute. We constrain the couplings of the theory by imposing CFT unitarity and positivity of energy (which we show to be equivalent to causality in the bulk) as well as positive-entropy bounds from the weak gravity conjecture. The thermodynamic properties of the dual plasma at finite chemical potential are studied in detail, and we find that exotic zeroth-order phase transitions may appear, but that many of them are ruled out by the physical constraints. We further compute the shear viscosity to entropy density ratio, and we show that it can be taken to zero while respecting all the constraints, providing that the chemical potential is large enough. We also obtain the charged Rényi entropies and we observe that the chemical potential always increases the amount of entanglement and that the usual properties of Rényi entropies are preserved if the physical constraints are met. Finally, we compute the scaling dimension and magnetic response of twist operators and we provide a holographic derivation of the universal relations between the expansion of these quantities and the coefficients of 〈JJ〉 and 〈TJJ〉.

Shape deformations of charged Rényi entropies from holography

Charged and symmetry-resolved Rényi entropies are entanglement measures quantifying the degree of entanglement within different charge sectors of a theory with a conserved global charge. We use holography to determine the dependence of charged Rényi entropies on small shape deformations away from a spherical or planar entangling surface in general dimensions. This dependence is completely characterized by a single coefficient appearing in the two point function of the displacement operator associated with the Rényi defect. We extract this coefficient using its relation to the one point function of the stress tensor in the presence of a deformed entangling surface. This is mapped to a holographic calculation in the background of a deformed charged black hole with hyperbolic horizon. We obtain numerical solutions for different values of the chemical potential and replica number n in various spacetime dimensions, as well as analytic expressions for small chemical potential near n = 1. When the Rényi defect becomes supersymmetric, we demonstrate a conjectured relation between the two point function of the displacement operator and the conformal weight of the twist operator.

Exact result in mathcal{N} = 4 SYM theory: generalised double-logarithmic equation

We present the new results for the generalised double-logarithmic equation, obtained from the analytical continuation of the seven-loop anomalous dimension of twist-2 operators in the planar mathcal{N} = 4 SYM theory. The double-logarithmic equation is related to the special asymptotic of the scattering amplitudes, when the large logarithms of the energy of scattering particles are appeared and should be summed in all order of perturbative theory. These large logarithms correspond to the poles of the analytically continued anomalous dimension. The generalised double-logarithmic equation includes the subleading logarithms. We have found, that the expansion of the generalised double-logarithmic equation can be ressumed in the form of rational functions with simple denominator. The solution of the generalised double-logarithmic equation provides a lot of information about the poles of the analytically continued anomalous dimension in all orders of perturbative theory. We have found also the generalised double-logarithmic equation for the analytically continued anomalous dimension near the value, which is related with BFKL-equation.

Partition functions and entanglement entropy: Weyl graviton and conformal higher spin fields

We establish the relation of partition functions of conformal higher spin fields on Weyl equivalent spaces in d = 4 dimension. We express the partition function of Weyl graviton and conformal higher spin fields as an integral over characters on S1× AdS3, S4, and AdS4. We observe that the partition function of conformal higher spins on hyperbolic cylinders differs from the partition function on S4 by the ‘edge’ contribution. The logarithmic coefficient obtained from the character integral of the partition function of conformal higher spins on AdS4 is the half of that obtained from the partition function on S4. We evaluate the entanglement entropy and the conformal dimension of the twist operator from the partition function on the hyperbolic cylinder. The conformal dimension of the co-dimension two twist operator enables us to find a linear relation between Hofman-Maldacena variables which we use to show the non-unitarity of the theory. We observe that the spectrum of the quasinormal modes of conformal higher spins obtained from the bulk character contains additional distinct states compared to the spectrum of unitary massless higher spin fields.

Twisted differential operators of negative level and prismatic crystals

We introduce twisted differential calculus of negative level and prove a descent theorem: Frobenius pullback provides an equivalence between finitely presented modules endowed with a topologically quasi-nilpotent twisted connection of level minus one and those of level zero. We explain how this is related to the existence of a Cartier operator on prismatic crystals. For the sake of readability, we limit ourselves to the case of dimension one.

Replica wormholes from Liouville theory

The replica wormholes are a key to the existence of the islands that play a central role in a recent proposal for the resolution of the black hole information paradox. In this paper, we study the replica wormholes in the JT gravity, a model of two-dimensional quantum gravity coupled to a non-dynamical dilaton, by making use of the 2d conformal field theory (CFT) description, namely, the Liouville theory coupled to the (2, p) minimal matter in the p → ∞ limit. In the Liouville CFT description, the replica wormholes are created by the twist operators and the gravitational part of the bulk entanglement entropy can be reproduced from the twist operator correlators. We propose the precise dictionary and show how this correspondence works in detail.

Instanton-induced effects in interquark forces, light-front wave functions and formfactors

Exclusive processes are traditionally described by perturbative hard blocks and “distribution amplitudes" (DAs), matrix elements of operators of various chiral structure and twist. One paper (with I.Zahed) calculate instanton contribution to hard blocks, which is found comparable to perturbative one in few-GeV2 Q2 region of interest. Another paper aims at comprehensive wave functions of mesons, baryons and pentaquarks. The last ones are also included as 5-quark component of the baryons. The calculation, using ’t Hooft operator, gives x-dependence and magnitude of the antiquark PDF. It explains long standing issue of strong flavor asymmetry of antiquark sea. The third paper (also with I.Zahed) is semi-review on the instanton-sphaleron processes in QCD and electroweak theories, with emphasis on their possible experimental observation via double diffractive events at LHC and RHIC. Insert your english abstract here.

Asymptotically free AdS3/CFT2

We propose a new AdS3/CFT2 duality, in which the bulk string theory has a target spacetime AdS3 times a squashed three-sphere {mathbbm{S}}_{flat}^3 , and the dual CFT2 is a symmetric product of sigma models on ℝϕ× {mathbbm{S}}_{flat}^3 , deformed by a ϕ-dependent ℤ2 twist operator. The duality maps the asymptotic region of AdS3 to the region ϕ → ∞, where the twist interaction in the CFT2 turns off. The AdS3 backgrounds in question have RAdS< ℓs, and so lie on the string side of the string/black hole correspondence transition. As a consequence, the high energy density of states consists of a string gas in AdS3 rather than an ensemble of BTZ black holes. This property allows us to derive the dual CFT2 by a systematic analysis of the worldsheet string theory on AdS3.

One-loop string corrections for AdS Kaluza-Klein amplitudes

We discuss the string corrections to one-loop amplitudes in AdS5×S5, focussing on their expressions in Mellin space. We present the leading (α′)3 corrections to the family of correlators leftlangle {mathcal{O}}_2{mathcal{O}}_2{mathcal{O}}_p{mathcal{O}}_prightrangle at one loop and begin the exploration of the form of correlators with multiple channels. From these correlators we extract some string corrections to one- loop anomalous dimensions of families of operators of low twist.

Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra

We consider a class of exponentials in the Weyl-Heisenberg algebra with exponents of type at most linear in coordinates and arbitrary functions of momenta. They are expressed in terms of normal ordering where coordinates stand to the left from momenta. Exponents appearing in normal ordered form satisfy differential equations with boundary conditions that could be solved perturbatively order by order. Two propositions are presented for the Weyl-Heisenberg algebra in 2 dimensions and their generalizations in higher dimensions. These results can be applied to arbitrary noncommutative spaces for construction of star products, coproducts of momenta and twist operators. They can also be related to the BCH formula.

Differential operators on quantized flag manifolds at roots of unity III

We describe the cohomology of the sheaf of twisted differential operators on the quantized flag manifold at a root of unity whose order is a prime power. It follows from this and our previous results that for the De Concini-Kac type quantized enveloping algebra, where the parameter q is specialized to a root of unity whose order is a prime power, the number of irreducible modules with a certain specified central character coincides with the dimension of the total cohomology group of the corresponding Springer fiber. This gives a weak version of a conjecture of Lusztig concerning non-restricted representations of the quantized enveloping algebra.

Holographic entanglement entropy in AdS3/WCFT

In this paper, we consider AdS3 with Compère-Song-Strominger (CSS) boundary conditions, under which the dual field theory is warped conformal field theory (WCFT), featuring a Virasoro-Kac-Moody algebra. We provide a holographic dual picture of the single interval entanglement entropy in WCFT in the bulk AdS3. We explicitly show that the bulk object captures the entanglement entropy in WCFT is a massive spinning particle's worldline that anchored on the boundary of the interval. Given the mass and spin of the particle as functions of quantum numbers of the twist operator in WCFT, the on-shell worldline action will match the entanglement entropy in WCFT.

Narain to Narnia

We generalize the holographic correspondence between topological gravity coupled to an abelian Chern-Simons theory in three dimensions and an ensemble average of Narain's family of massless free bosons in two dimensions, discovered by Afkhami-Jeddi et al. and by Maloney and Witten. We find that the correspondence also works for toroidal orbifolds but not for K3 or Calabi-Yau sigma-models and not always for the minimal models. We conjecture that the correspondence requires that the central charge is equal to the critical central charge defined by the asymptotic density of states of the chiral algebra. For toroidal orbifolds, we extend the holographic correspondence to correlation functions of twist operators by using topological properties of rational tangles in the three-dimensional ball, which represent configurations of vortices associated to a discrete gauge symmetry.

Holographic correlators with multi-particle states

We derive the connected tree-level part of 4-point holographic correlators in AdS3 × S3 × mathcal{M} (where mathcal{M} is T4 or K3) involving two multi-trace and two single-trace operators. These connected correlators are obtained by studying a heavy-heavy-light-light correlation function in the formal limit where the heavy operators become light. These results provide a window into higher-point holographic correlators of single-particle operators. We find that the correlators involving multi-trace operators are compactly written in terms of Bloch-Wigner-Ramakrishnan functions — particular linear combinations of higher-order polylogarithm functions. Several consistency checks of the derived expressions are performed in various OPE channels. We also extract the anomalous dimensions and 3-point couplings of the non-BPS double-trace operators of lowest twist at order 1/c and find some positive anomalous dimensions at spin zero and two in the K3 case.

N-point correlators of twist-2 operators in SU(N) Yang-Mills theory to the lowest perturbative order

We compute, to the lowest perturbative order in SU(N) Yang-Mills theory, n-point correlators in the coordinate and momentum representation of the gauge-invariant twist-2 operators with maximal spin along the p+ direction, both in Minkowskian and — by analytic continuation — Euclidean space-time. We also construct the corresponding generating functionals. Remarkably, they have the structure of the logarithm of a functional determinant of the identity plus a term involving the effective propagators that act on the appropriate source fields.