Searcharxiv⌕ Search

arXiv subjects

Damiano Anselmi

Publications and source records attributed to Damiano Anselmi.

90 records · Page 5Linked to original sources
arXiv2004

Finiteness of quantum gravity coupled with matter in three spacetime dimensions

As it stands, quantum gravity coupled with matter in three spacetime dimensions is not finite. In this paper I show that an algorithmic procedure that makes it finite exists, under certain conditions. To achieve this result, gravity is coupled with an interacting conformal field theory C. The Newton constant and the marginal parameters of C are taken as independent couplings. The values of the other irrelevant couplings are determined iteratively in the loop- and energy-expansions, imposing that their beta functions vanish. The finiteness equations are solvable thanks to the following properties: the beta functions of the irrelevant couplings have a simple structure; the irrelevant terms made with the Riemann tensor can be reabsorbed by means of field redefinitions; the other irrelevant terms have, generically, non-vanishing anomalous dimensions. The perturbative expansion is governed by an effective Planck mass that takes care of the interactions in the matter sector. As an example, I study gravity coupled with Chern-Simons U(1) gauge theory with massless fermions, solve the finiteness equations and determine the four-fermion couplings to two-loop order. The construction of this paper does not immediately apply to four-dimensional quantum gravity.

hep-th↗
arXiv2004

Renormalization of quantum gravity coupled with matter in three dimensions

In three spacetime dimensions, where no graviton propagates, pure gravity is known to be finite. It is natural to inquire whether finiteness survives the coupling with matter. Standard arguments ensure that there exists a subtraction scheme where no Lorentz-Chern-Simons term is generated by radiative corrections, but are not sufficiently powerful to ensure finiteness. Therefore, it is necessary to perform an explicit (two-loop) computation in a specific model. I consider quantum gravity coupled with Chern-Simons U(1) gauge theory and massless fermions and show that renormalization originates four-fermion divergent vertices at the second loop order. I conclude that quantum gravity coupled with matter, as it stands, is not finite in three spacetime dimensions.

hep-th↗
arXiv2003

Consistent irrelevant deformations of interacting conformal field theories

I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale ("quasi-finite"). They are made of an infinite number of lagrangian terms and a finite number of independent parameters that renormalize coherently. The coefficients of the irrelevant terms are determined imposing that the beta functions of the dimensionless combinations of couplings vanish ("quasi-finiteness equations"). The expansion in powers of the energy is meaningful for energies much smaller than an effective Planck mass. Multiple deformations can be considered also. I study the general conditions to have non-trivial solutions. As an example, I construct the Pauli deformation of the IR fixed point of massless non-Abelian Yang-Mills theory with N_c colors and N_f <~ 11N_c/2 flavors and compute the couplings of the term F^3 and the four-fermion vertices. Another interesting application is the construction of finite chiral irrelevant deformations of N=2 and N=4 superconformal field theories. The results of this paper suggest that power-counting non-renormalizable theories might play a role in the description of fundamental physics.

hep-th↗
arXiv2003

Inequalities for trace anomalies, length of the RG flow, distance between the fixed points and irreversibility

I discuss several issues about the irreversibility of the RG flow and the trace anomalies c, a and a'. First I argue that in quantum field theory: i) the scheme-invariant area Delta(a') of the graph of the effective beta function between the fixed points defines the length of the RG flow; ii) the minimum of Delta(a') in the space of flows connecting the same UV and IR fixed points defines the (oriented) distance between the fixed points; iii) in even dimensions, the distance between the fixed points is equal to Delta(a)=a_UV-a_IR. In even dimensions, these statements imply the inequalities 0 =< Delta(a)=< Delta(a') and therefore the irreversibility of the RG flow. Another consequence is the inequality a =< c for free scalars and fermions (but not vectors), which can be checked explicitly. Secondly, I elaborate a more general axiomatic set-up where irreversibility is defined as the statement that there exist no pairs of non-trivial flows connecting interchanged UV and IR fixed points. The axioms, based on the notions of length of the flow, oriented distance between the fixed points and certain "oriented-triangle inequalities", imply the irreversibility of the RG flow without a global a function. I conjecture that the RG flow is irreversible also in odd dimensions (without a global a function). In support of this, I check the axioms of irreversibility in a class of d=3 theories where the RG flow is integrable at each order of the large N expansion.

hep-th↗
arXiv2003

Absence of higher derivatives in the renormalization of propagators in quantum field theories with infinitely many couplings

I study some aspects of the renormalization of quantum field theories with infinitely many couplings in arbitrary space-time dimensions. I prove that when the space-time manifold admits a metric of constant curvature the propagator is not affected by terms with higher derivatives. More generally, certain lagrangian terms are not turned on by renormalization, if they are absent at the tree level. This restricts the form of the action of a non-renormalizable theory, and has applications to quantum gravity. The new action contains infinitely many couplings, but not all of the ones that might have been expected. In quantum gravity, the metric of constant curvature is an extremal, but not a minimum, of the complete action. Nonetheless, it appears to be the right perturbative vacuum, at least when the curvature is negative, suggesting that the quantum vacuum has a negative asymptotically constant curvature. The results of this paper give also a set of rules for a more economical use of effective quantum field theories and suggest that it might be possible to give mathematical sense to theories with infinitely many couplings at high energies, to search for physical predictions.

hep-th↗
arXiv1996

Quantum Topological Invariants, Gravitational Instantons and the Topological Embedding

Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is particularly meaningful in the class of Weyl instantons, is introduced. The topological embedding, a theoretical framework for constructing physical amplitudes that are well-defined order by order in perturbation theory around instantons, is explicitly applied to the computation of the correlation functions of Dirac fermions in a punctured gravitational background, as well as to the most general QED and QCD amplitude. Various alternatives are worked out, discussed and compared. The quantum background affects the propagation by generating a certain effective ``quantum'' metric. The topological embedding could represent a new chapter of quantum field theory.

hep-th↗
arXiv1995

Topological field theory and physics

Topological Yang-Mills theory with the Belavin-Polyakov-Schwarz-Tyupkin $SU(2)$ instanton is solved completely, revealing an underlying multi-link intersection theory. Link invariants are also shown to survive the coupling to a certain kind of matter (hyperinstantons). The physical relevance of topological field theory and its invariants is discovered. By embedding topological Yang-Mills theory into pure Yang-Mills theory, it is shown that the topological version TQFT of a quantum field theory QFT allows us to formulate consistently the perturbative expansion of QFT in the topologically nontrivial sectors. In particular, TQFT classifies the set of good measures over the instanton moduli space and solves the inconsistency problems of the previous approaches. The qualitatively new physical implications are pointed out. Link numbers in QCD are related to a non abelian analogoue of the Aharonov-Bohm effect.

hep-th↗
arXiv1995

Anomalies in Instanton Calculus

I develop a formalism for solving topological field theories explicitly, in the case when the explicit expression of the instantons is known. I solve topological Yang-Mills theory with the $k=1$ Belavin {\sl et al.} instanton and topological gravity with the Eguchi-Hanson instanton. It turns out that naively empty theories are indeed nontrivial. Many unexpected interesting hidden quantities (punctures, contact terms, nonperturbative anomalies with or without gravity) are revealed. Topological Yang-Mills theory with $G=SU(2)$ is not just Donaldson theory, but contains a certain {\sl link} theory. Indeed, local and non-local observables have the property of {\sl marking} cycles. From topological gravity one learns that an object can be considered BRST exact only if it is so all over the moduli space ${\cal M}$, boundary included. Being BRST exact in any interior point of ${\cal M}$ is not sufficient to make an amplitude vanish. Presumably, recursion relations and hierarchies can be found to solve topological field theories in four dimensions, in particular topological Yang-Mills theory with $G=SU(2)$ on ${\bf R}^4$ and topological gravity on ALE manifolds.

hep-th↗
arXiv1994

Gauged Hyperinstantons and Monopole Equations

The monopole equations in the dual abelian theory of the N=2 gauge-theory, recently proposed by Witten as a new tool to study topological invariants, are shown to be the simplest elements in a class of instanton equations that follow from the improved topological twist mechanism introduced by the authors in previous papers. When applied to the N=2 sigma-model, this twisting procedure suggested the introduction of the so-called hyperinstantons, or triholomorphic maps. When gauging the sigma-model by coupling it to the vector multiplet of a gauge group G, one gets gauged hyperinstantons that reduce to the Seiberg-Witten equations in the flat case and G=U(1). The deformation of the self-duality condition on the gauge-field strength due to the monopole-hyperinstanton is very similar to the deformation of the self-duality condition on the Riemann curvature previously observed by the authors when the hyperinstantons are coupled to topological gravity. In this paper the general form of the hyperinstantonic equations coupled to both gravity and gauge multiplets is presented.

hep-th↗
arXiv1994

Nodes as Composite Operators in Matrix Models

Riemann surfaces with nodes can be described by introducing simple composite operators in matrix models. In the case of the Kontsevich model, it is sufficient to add the quadratic, but ``non-propagating'', term (tr[X])^2 to the Lagrangian. The corresponding Jenkins-Strebel differentials have pairwise identified simple poles. The result is in agreement with a conjecture formulated by Kontsevich and recently investigated by Arbarello and Cornalba that the set ${\cal M}_{m*,s}$ of ribbon graphs with s faces and $m*=(m_0,m_1,\ldots,m_j,\ldots)$ vertices of valencies $(1,3,\ldots,2j+1,\ldots)$ ``can be expressed in terms of Mumford-Morita classes'': one gets an interpretation for univalent vertices. I also address the possible relationship with a recently formulated theory of constrained topological gravity.

hep-th↗
arXiv1994

More on the Subtraction Algorithm

We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on redefinitions $δλ$ of the parameters $λ$ of the classical Lagrangian and canonical transformations, by generalizing a well- known conjecture on the form of the divergent terms. We also show that it is possible to reach a complete control on the effects of the subtraction algorithm on the space ${\cal M}_{gf}$ of the gauge-fixing parameters. A principal fiber bundle ${\cal E}\rightarrow {\cal M}_{gf}$ with a connection $ω_1$ is defined, such that the canonical transformations are gauge transformations for $ω_1$. This provides an intuitive geometrical description of the fact the on shell physical amplitudes cannot depend on ${\cal M}_{gf}$. A geometrical description of the effect of the subtraction algorithm on the space ${\cal M}_{ph}$ of the physical parameters $λ$ is also proposed. At the end, the full subtraction algorithm can be described as a series of diffeomorphisms on ${\cal M}_{ph}$, orthogonal to ${\cal M}_{gf}$ (under which the action transforms as a scalar), and gauge transformations on ${\cal E}$. In this geometrical context, a suitable concept of predictivity is formulated. We give some examples of (unphysical) toy models that satisfy this requirement, though being neither power counting renormalizable, nor finite.

hep-th↗
arXiv1994

Constrained Topological Field Theory

We derive a model of constrained topological gravity, a theory recently introduced by us through the twist of N=2 Liouville theory, starting from the general BRST algebra and imposing the moduli space constraint as a gauge fixing. To do this, it is necessary to introduce a formalism that allows a careful treatment of the global and the local degrees of freedom of the fields. Surprisingly, the moduli space constraint arises from the simplest and most natural gauge-fermion ({\sl antighost} $\times$ {\sl Lagrange multiplier}), confirming the previous results. The simplified technical set-up provides a deeper understanding for constrained topological gravity and a convenient framework for future investigations, like the matter coupling and the analysis of the effects of the constraint on the holomorphic anomaly.

hep-th↗
arXiv1993

Predictivity and Nonrenormalizability

We consider the problem of removing the divergences in an arbitrary gauge-field theory (possibly nonrenormalizable). We show that this can be achieved by performing, order by order in the loop expansion, a redefinition of some parameters (possibly infinitely many) and a canonical transformation (in the sense of Batalin and Vilkovisky) of fields and BRS sources. Gauge-invariance is turned into a suitable quantum generalization of BRS-invariance. We define quantum observables and study their properties. We apply the result to renormalizable gauge-field theories that are gauge-fixed with a nonrenormalizable gauge-fixing and prove that their predictivity is retained. A corollary is that topological field theories are predictive. Analogies and differences with the formalisms of classical and quantum mechanics are pointed out.

hep-th↗
arXiv1993

Covariant Pauli-Villars Regularization of Quantum Gravity at the One Loop Order

We study a regularization of the Pauli-Villars kind of the one loop gravitational divergences in any dimension. The Pauli-Villars fields are massive particles coupled to gravity in a covariant and nonminimal way, namely one real tensor and one complex vector. The gauge is fixed by means of the unusual gauge-fixing that gives the same effective action as in the context of the background field method. Indeed, with the background field method it is simple to see that the regularization effectively works. On the other hand, we show that in the usual formalism (non background) the regularization cannot work with each gauge-fixing.In particular, it does not work with the usual one. Moreover, we show that, under a suitable choice of the Pauli-Villars coefficients, the terms divergent in the Pauli-Villars masses can be corrected by the Pauli-Villars fields themselves. In dimension four, there is no need to add counterterms quadratic in the curvature tensor to the Einstein action (which would be equivalent to the introduction of new coupling constants). The technique also works when matter is coupled to gravity. We discuss the possible consequences of this approach, in particular the renormalization of Newton's coupling constant and the appearance of two parameters in the effective action, that seem to have physical implications.

hep-th↗
arXiv1993

Topological Sigma-Models in Four Dimensions and Triholomorphic Maps

It is well-known that topological sigma-models in 2 dimensions constitute a path-integral approach to the study of holomorphic maps from a Riemann surface S to an almost complex manifold K, the most interesting case being that where K is a Kahler manifold. We show that, in the same way, topological sigma-models in 4 dimensions introduce a path integral approach to the study of triholomorphic maps q:M-->N from a 4dimensional Riemannian manifold M to an almost quaternionic manifold N. The most interesting cases are those where M, N are hyperKahler or quaternionic Kahler. BRST-cohomology translates into intersection theory in the moduli-space of this new class of instantonic maps, named by us hyperinstantons. The definition of triholomorphicity that we propose is expressed by the equation q_*-J_u q_* j_u = 0, u=1,2,3, where {j_u} is an almost quaternionic structure on M and {J_u} is an almost quaternionic structure on N. This is a generalization of the Cauchy-Fueter equations. For M, N hyperKahler, this generalization naturally arises by obtaining the topological sigma-model as a twisted version of the N=2 globally supersymmetric sigma-model. We discuss various examples of hyperinstantons, in particular on the torus and the K3 surface. We also analyse the coupling of the topological sigma-model to topological gravity. The study of

hep-th↗
arXiv1992

Topological Twist in Four Dimensions, R-Duality and Hyperinstantons

In this paper we continue the programme of topologically twisting N=2 theories in D=4, focusing on the coupling of vector multiplets to N=2 supergravity. We show that in the minimal case, namely when the special geometry prepotential F(X) is a quadratic polynomial, the theory has a so far unknown on shell U(1) symmetry, that we name R-duality. R-duality is a generalization of the chiral-dual on shell symmetry of N=2 pure supergravity and of the R-symmetry of N=2 super Yang-Mills theory. Thanks to this, the theory can be topologically twisted and topologically shifted, precisely as pure N=2 supergravity, to yield a natural coupling of topological gravity to topological Yang-Mills theory. The gauge-fixing condition that emerges from the twisting is the self- duality condition on the gauge field-stength and on the spin connection. Hence our theory reduces to intersection theory in the moduli-space of gauge instantons living in gravitational instanton backgrounds. We remark that the topological Yang-Mills theory we obtain by taking the flat space limit of our gravity coupled Lagrangian is different from the Donaldson theory constructed by Witten. Whether this difference is substantial and what its geometrical implications may be is yet to be seen. We also discuss the topological twist of the hypermultiplets leading to topological quaternionic $σ$-models. The instantons of these models, named by us hyperinstantons, correspond to a notion of triholomorphic mappings discussed in the paper.

hep-th↗
arXiv1992

Twisted N=2 Supergravity as Topological Gravity in Four Dimensions

We show that the BRST quantum version of pure D=4 N=2 supergravity can be topologically twisted, to yield a formulation of topological gravity in four dimensions. The topological BRST complex is just a rearrangement of the old BRST complex, that partly modifies the role of physical and ghost fields: indeed, the new ghost number turns out to be the sum of the old ghost number plus the internal U(1) charge. Furthermore, the action of N=2 supergravity is retrieved from topological gravity by choosing a gauge fixing that reduces the space of physical states to the space of gravitational instanton configurations, namely to self-dual spin connections. The descent equations relating the topological observables are explicitly exhibited and discussed. Ours is a first step in a programme that aims at finding the topological sector of matter coupled N=2 supergravity, viewed as the effective Lagrangian of type II superstrings and, as such, already related to 2D topological field-theories. As it stands the theory we discuss may prove useful in describing gravitational instantons moduli-spaces.

hep-th↗