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D. Anselmi

Publications and source records attributed to D. Anselmi.

At least 19 recordsLinked to original sources
arXiv2003

Search for flow invariants in even and odd dimensions

A flow invariant in quantum field theory is a quantity that does not depend on the flow connecting the UV and IR conformal fixed points. We study the flow invariance of the most general sum rule with correlators of the trace Theta of the stress tensor. In even (four and six) dimensions we recover the results known from the gravitational embedding. We derive the sum rules for the trace anomalies a and a' in six dimensions. In three dimensions, where the gravitational embedding is more difficult to use, we find a non-trivial vanishing relation for the flow integrals of the three- and four-point functions of Theta. Within a class of sum rules containing finitely many terms, we do not find a non-vanishing flow invariant of type a in odd dimensions. We comment on the implications of our results.

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arXiv2002

"Integrability" of RG flows and duality in three dimensions in the 1/N expansion

I study some classes of RG flows in three dimensions that are classically conformal and have manifest g -> 1/g dualities. The RG flow interpolates between known (four-fermion, Wilson-Fischer, phi_3^6) and new interacting fixed points. These models have two remarkable properties: i) the RG flow can be integrated for arbitrarily large values of the couplings g at each order of the 1/N expansion; ii) the duality symmetries are exact at each order of the 1/N expansion. I integrate the RG flow explicitly to the order O(1/N), write correlators at the leading-log level and study the interpolation between the fixed points. I examine how duality is implemented in the regularized theory and verified in the results of this paper.

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arXiv2001

Kinematic sum rules for trace anomalies

I derive a procedure to generate sum rules for the trace anomalies a and a'. Linear combinations of Delta a = a_UV-a_IR and Delta a' = a'_UV-a'_IR are expressed as multiple flow integrals of the two-, three- and four-point functions of the trace of the stress tensor. Eliminating Delta a', universal flow invariants are obtained, in particular sum rules for Delta a. The formulas hold in the most general renormalizable quantum field theory (unitary or not), interpolating between UV and IR conformal fixed points. I discuss the relevance of these sum rules for the issue of the irreversibility of the RG flow. The procedure can be generalized to derive sum rules for the trace anomaly c.

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arXiv2001

A note on the improvement ambiguity of the stress tensor and the critical limits of correlation functions

I study various properties of the critical limits of correlators containing insertions of conserved and anomalous currents. In particular, I show that the improvement term of the stress tensor can be fixed unambiguously, studying the RG interpolation between the UV and IR limits. The removal of the improvement ambiguity is encoded in a variational principle, which makes use of sum rules for the trace anomalies a and a'. Compatible results follow from the analysis of the RG equations. I perform a number of self-consistency checks and discuss the issues in a large set of theories.

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arXiv2001

A universal flow invariant in quantum field theory

A flow invariant is a quantity depending only on the UV and IR conformal fixed points and not on the flow connecting them. Typically, its value is related to the central charges a and c. In classically-conformal field theories, scale invariance is broken by quantum effects and the flow invariant a_{UV}-a_{IR} is measured by the area of the graph of the beta function between the fixed points. There exists a theoretical explanation of this fact. On the other hand, when scale invariance is broken at the classical level, it is empirically known that the flow invariant equals c_{UV}-c_{IR} in massive free-field theories, but a theoretical argument explaining why it is so is still missing. A number of related open questions are answered here. A general formula of the flow invariant is found, which holds also when the stress tensor has improvement terms. The conditions under which the flow invariant equals c_{UV}-c_{IR} are identified. Several non-unitary theories are used as a laboratory, but the conclusions are general and an application to the Standard Model is addressed. The analysis of the results suggests some new minimum principles, which might point towards a better understanding of quantum field theory.

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arXiv2000

Large-N expansion, conformal field theory and renormalization-group flows in three dimensions

I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-N approach and a modified dimensional-regularization technique. Bosons are associated with composite operators and their propagators are dynamically generated by fermion bubbles. Renormalization-group flows between pairs of interacting fixed points satisfy a set of non-perturbative g <-> 1/g dualities. There is an exact relation between the beta function and the anomalous dimension of the composite boson. Non-Abelian gauge fields have a non-renormalized and quantized gauge coupling, although no Chern-Simons term is present. A problem of the naive dimensional-regularization technique for these theories is uncovered and removed with a non-local, evanescent, non-renormalized kinetic term. The models are expected to be a fruitful arena for the study of odd-dimensional conformal field theory.

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arXiv2000

Irreversibility and higher-spin conformal field theory

I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.

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arXiv2000

A Note on the Holographic Beta and C Functions

The holographic RG flow in AdS/CFT correspondence naturally defines a holographic scheme in which the central charge c and the beta function are related by a universal formula. We perform some checks of that formula and we compare it with quantum field theory expectations. We discuss alternative definitions of the c-function. In particular, we compare, for a particular supersymmetric flow, the holographic c-function with the central charge computed directly from the two-point function of the stress-energy tensor.

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arXiv2000

Higher-spin current multiplets in operator-product expansions

Various formulas for currents with arbitrary spin are worked out in general space-time dimension, in the free field limit and, at the bare level, in presence of interactions. As the n-dimensional generalization of the (conformal) vector field, the (n/2-1)-form is used. The two-point functions and the higher-spin central charges are evaluated at one loop. As an application, the higher-spin hierarchies generated by the stress-tensor operator-product expansion are computed in supersymmetric theories. The results exhibit an interesting universality.

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arXiv1999

Towards the classification of conformal field theories in arbitrary even dimension

I identify the class of even-dimensional conformal field theories that is most similar to two-dimensional conformal field theory. In this class the formula, elaborated recently, for the irreversibility of the renormalization-group flow applies also to massive flows. This implies a prediction for the ratio between the coefficient of the Euler density in the trace anomaly (charge a) and the stress-tensor two-point function (charge c). More precisely, the trace anomaly in external gravity is quadratic in the Ricci tensor and the Ricci scalar and contains a unique central charge. I check the prediction in detail in four, six and eight dimensions, and then in arbitrary even dimension.

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arXiv1999

Quantum irreversibility in arbitrary dimension

Some recent ideas are generalized from four dimensions to the general dimension n. In quantum field theory, two terms of the trace anomaly in external gravity, the Euler density G_n and Box^{n/2-1}R, are relevant to the problem of quantum irreversibility. By adding the divergence of a gauge-invariant current, G_n can be extended to a new notion of Euler density, linear in the conformal factor. We call it pondered Euler density. This notion relates the trace-anomaly coefficients a and a' of G_n and Box^{n/2-1}R in a universal way (a=a') and gives a formula expressing the total RG flow of a as the invariant area of the graph of the beta function between the fixed points. I illustrate these facts in detail for n=6 and check the prediction to the fourth-loop order in the phi^3-theory. The formula of quantum irreversibility for general n even can be extended to n odd by dimensional continuation. Although the trace anomaly in external gravity is zero in odd dimensions, I show that the odd-dimensional formula has a predictive content.

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arXiv1999

Anomalies, Unitarity and Quantum Irreversibility

The trace anomaly in external gravity is the sum of three terms at criticality: the square of the Weyl tensor, the Euler density and Box R, with coefficients, properly normalized, called c, a and a', the latter being ambiguously defined by an additive constant. Considerations about unitarity and positivity properties of the induced actions allow us to show that the total RG flows of a and a' are equal and therefore the a'-ambiguity can be consistently removed through the identification a'=a. The picture that emerges clarifies several long-standing issues. The interplay between unitarity and renormalization implies that the flux of the renormalization group is irreversible. A monotonically decreasing a-function interpolating between the appropriate values is naturally provided by a'. The total a-flow is expressed non-perturbatively as the invariant (i.e. scheme-independent) area of the graph of the beta function between the fixed points. We test this prediction to the fourth loop order in perturbation theory, in QCD with Nf ~< 11/2 Nc and in supersymmetric QCD. There is agreement also in the absence of an interacting fixed point (QED and phi^4-theory). Arguments for the positivity of a are also discussed.

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arXiv1998

Subleading Corrections and Central Charges in the AdS/CFT Correspondence

We explore subleading contributions to the two basic central charges c and a of four-dimensional conformal field theories in the AdS/CFT scheme. In particular we probe subleading corrections to the difference c-a from the string-theory side. In the N=4 CFT, c-a vanish identically consistently with the string-theory expectations. However, for N=1 and N=2 CFTs, the U_R(1) anomaly, which is proportional to c-a, is subleading in the large N limit for theories in the AdS/CFT context and one expects string one-loop R^2 and B \wedge R \wedge R terms in the low energy effective action. We identify these terms as coming from the R^4 terms. Similar considerations apply to the U_R(1)^3 anomaly which is, however, subleading only for N=2 theories. As a result, a string one-loop term B \wedge F \wedge F should exist in the low energy effective action of the N=4 five-dimensional supergravity. The U_R(1)^3 term is leading for the N=1 CFT and it is indeed present in the N=2 five-dimensional supergravity.

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arXiv1998

The N=4 Quantum Conformal Algebra

We determine the spectrum of currents generated by the operator product expansion of the energy-momentum tensor in N=4 super-symmetric Yang-Mills theory. Up to the regular terms and in addition to the multiplet of the stress tensor, three current multiplets appear, Sigma, Xi and Upsilon, starting with spin 0, 2 and 4, respectively. The OPE's of these new currents generate an infinite tower of current multiplets, one for each even spin, which exhibit a universal structure, of length 4 in spin units, identified by a two-parameter rational family. Using higher spin techniques developed recently for conformal field theories, we compute the critical exponents of Sigma, Xi and Upsilon in the TT OPE and prove that the essential structure of the algebra holds at arbitrary coupling. We argue that the algebra closes in the strongly coupled large-$N_c$ limit. Our results determine the quantum conformal algebra of the theory and answer several questions that previously remained open.

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arXiv1998

Quantum Conformal Algebras and Closed Conformal Field Theory

We investigate the quantum conformal algebras of N=2 and N=1 supersymmetric gauge theories. Phenomena occurring at strong coupling are analysed using the Nachtmann theorem and very general, model-independent, arguments. The results lead us to introduce a novel class of conformal field theories, identified by a closed quantum conformal algebra. We conjecture that they are the exact solution to the strongly coupled large-N_c limit of the open conformal field theories. We study the basic properties of closed conformal field theory and work out the operator product expansion of the conserved current multiplet T. The OPE structure is uniquely determined by two central charges, c and a. The multiplet T does not contain just the stress-tensor, but also R-currents and finite mass operators. For this reason, the ratio c/a is different from 1. On the other hand, an open algebra contains an infinite tower of non-conserved currents, organized in pairs and singlets with respect to renormalization mixing. T mixes with a second multiplet T* and the main consequence is that c and a have different subleading corrections. The closed algebra simplifies considerably at c=a, where it coincides with the N=4 one.

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arXiv1998

Theory of higher spin tensor currents and central charges

We study higher spin tensor currents in quantum field theory. Scalar, spinor and vector fields admit unique "improved" currents of arbitrary spin, traceless and conserved. Off-criticality as well as at interacting fixed points conservation is violated and the dimension of the current is anomalous. In particular, currents J^(s,I) with spin s between 0 and 5 (and a second label I) appear in the operator product expansion of the stress tensor. The TT OPE is worked out in detail for free fields; projectors and invariants encoding the space-time structure are classified. The result is used to write and discuss the most general OPE for interacting conformal field theories and off-criticality. Higher spin central charges c_(s,I) with arbitrary s are defined by higher spin channels of the many-point T-correlators and central functions interpolating between the UV and IR limits are constructed. We compute the one-loop values of all c_(s,I) and investigate the RG trajectories of quantum field theories in the conformal window following our approach. In particular, we discuss certain phenomena (perturbative and nonperturbative) that appear to be of interest, like the dynamical removal of the I-degeneracy. Finally, we address the problem of formulating an action principle for the RG trajectory connecting pairs of CFT's as a way to go beyond perturbation theory.

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arXiv1997

Positivity Constraints on Anomalies in Supersymmetric Gauge Theories

The relation between the trace and R-current anomalies in supersymmetric theories implies that the U$(1)_RF^2$, U$(1)_R$ and U$(1)_R^3$ anomalies which are matched in studies of N=1 Seiberg duality satisfy positivity constraints. Some constraints are rigorous and others conjectured as four-dimensional generalizations of the Zamolodchikov $c$-theorem. These constraints are tested in a large number of N=1 supersymmetric gauge theories in the non-Abelian Coulomb phase, and they are satisfied in all renormalizable models with unique anomaly-free R-current, including those with accidental symmetry. Most striking is the fact that the flow of the Euler anomaly coefficient, $a_{UV}-a_{IR}$, is always positive, as conjectured by Cardy.

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