arXiv subjects

S. Hohenegger

Publications and source records attributed to S. Hohenegger.

17 recordsLinked to original sources

arXiv2023

Positivity Conditions for Generalised Schwarzschild Space-Times

We analyse the impact of positivity conditions on static spherically symmetric deformations of the Schwarzschild space-time. The metric is taken to satisfy, at least asymptotically, the Einstein equation in the presence of a non-trivial stress-energy tensor, on which we impose various physicality conditions. We systematically study and compare the impact of these conditions on the space-time deformations. The universal nature of our findings applies to both classical and quantum metric deformations with and without event horizons. We further discuss minimal realisations of the asymptotic stress energy tensor in terms of physical fields. Finally, we illustrate our results by discussing concrete models of quantum black holes.

gr-qc↗

arXiv2017

Monodromy Relations in Higher-Loop String Amplitudes

New monodromy relations of loop amplitudes are derived in open string theory. We particularly study N-point one-loop amplitudes described by a world-sheet cylinder (planar and non-planar) and derive a set of relations between subamplitudes of different color orderings. Various consistency checks are performed by matching alpha'-expansions of planar and non-planar amplitudes involving elliptic iterated integrals with the resulting periods giving rise to two sets of multiple elliptic zeta values. The latter refer to the two homology cycles on the once-punctured complex elliptic curve and the monodromy equations provide relations between these two sets of multiple elliptic zeta values. Furthermore, our monodromy relations involve new objects for which we present a tentative interpretation in terms of open string scattering amplitudes in the presence of a non-trivial gauge field flux. Finally, we provide an outlook on how to generalize the new monodromy relations to the non-oriented case and beyond the one-loop level. Comparing a subset of our results with recent findings in the literature we find therein several serious issues related to the structure and significance of monodromy phases and the relevance of missed contributions from contour integrations.

hep-th↗

arXiv2014

N=4 superconformal Ward identities for correlation functions

In this paper we study the four-point correlation function of the energy-momentum supermultiplet in theories with N=4 superconformal symmetry in four dimensions. We present a compact form of all component correlators as an invariant of a particular abelian subalgebra of the N=4 superconformal algebra. This invariant is unique up to a single function of the conformal cross-ratios which is fixed by comparison with the correlation function of the lowest half-BPS scalar operators. Our analysis is independent of the dynamics of a specific theory, in particular it is valid in N=4 super Yang-Mills theory for any value of the coupling constant. We discuss in great detail a subclass of component correlators, which is a crucial ingredient for the recent study of charge-flow correlations in conformal field theories. We compute the latter explicitly and elucidate the origin of the interesting relations among different types of flow correlations previously observed in arXiv:1309.1424.

hep-th↗

arXiv2014

Event shapes in N=4 super-Yang-Mills theory

We study event shapes in N=4 SYM describing the angular distribution of energy and R-charge in the final states created by the simplest half-BPS scalar operator. Applying the approach developed in the companion paper arXiv:1309.0769, we compute these observables using the correlation functions of certain components of the N=4 stress-tensor supermultiplet: the half-BPS operator itself, the R-symmetry current and the stress tensor. We present master formulas for the all-order event shapes as convolutions of the Mellin amplitude defining the correlation function of the half-BPS operators, with a coupling-independent kernel determined by the choice of the observable. We find remarkably simple relations between various event shapes following from N=4 superconformal symmetry. We perform thorough checks at leading order in the weak coupling expansion and show perfect agreement with the conventional calculations based on amplitude techniques. We extend our results to strong coupling using the correlation function of half-BPS operators obtained from the AdS/CFT correspondence.

hep-th↗

arXiv2014

From correlation functions to event shapes

We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and describe the angular distribution of global charges in outgoing radiation created from the vacuum by some source. The charge flow correlations can be expressed in terms of Wightman correlation functions in a certain limit. We explain how to compute these quantities starting from their Euclidean analogues by means of a non-trivial analytic continuation which, in the framework of CFT, can elegantly be performed in Mellin space. The relation between the charge flow correlations and Euclidean correlation functions can be reformulated directly in configuration space, bypassing the Mellin representation, as a certain Lorentzian double discontinuity of the correlation function integrated along the cuts. We illustrate the general formalism in N=4 SYM, making use of the well-known results on the four-point correlation function of half-BPS scalar operators. We compute the double scalar flow correlation in N=4 SYM, at weak and strong coupling and show that it agrees with known results obtained by different techniques. One of the remarkable features of the N=4 theory is that the scalar and energy flow correlations are proportional to each other. Imposing natural physical conditions on the energy flow correlations (finiteness, positivity and regularity), we formulate additional constraints on the four-point correlation functions in N=4 SYM that should be valid at any coupling and away from the planar limit.

hep-th↗

arXiv2013

Energy-energy correlations in N=4 SYM

We present a new approach to computing energy-energy correlations in gauge theories that exploits their relation to correlation functions and bypasses the use of scattering amplitudes. We illustrate its power by calculating energy-energy correlations in the maximally supersymmetric Yang-Mills theory (N=4 SYM) in the next-to-leading order approximation.

hep-th↗

arXiv2013

Worldsheet Realization of the Refined Topological String

A worldsheet realization of the refined topological string is proposed in terms of physical string amplitudes that compute generalized N=2 F-terms of the form F_{g,n} W^{2g}Y^{2n} in the effective supergravity action. These terms involve the chiral Weyl superfield W and a superfield Y defined as an N=2 chiral projection of a particular anti-chiral T-bar vector multiplet. In Heterotic and Type I theories, obtained upon compactification on the six-dimensional manifold K3xT2, T is the usual Kähler modulus of the T2 torus. These amplitudes are computed exactly at the one-loop level in string theory. They are shown to reproduce the correct perturbative part of the Nekrasov partition function in the field theory limit when expanded around an SU(2) enhancement point of the string moduli space. The two deformation parameters epsilon_- and epsilon_+ of the Omega-supergravity background are then identified with the constant field-strength backgrounds for the anti-self-dual graviphoton and self-dual gauge field of the T-bar vector multiplet, respectively.

hep-th↗

arXiv2011

BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form

We study BPS saturated one-loop amplitudes in type II string theory compactified on K3 x T^2. The classes of amplitudes we consider are only sensitive to the very basic topological data of the internal K3 manifold. As a consequence, the integrands of the former are related to the elliptic genus of K3, which can be decomposed into representations of the internal N=4 superconformal algebra. Depending on the precise choice of external states these amplitudes capture either only the contribution of the short multiplets or the full series including intermediate multiplets. In the latter case we can define a generating functional for the whole class, which we show is given by the weight ten Igusa cusp form chi_{10} of Sp(4,Z). We speculate on possible algebraic implications of our result on the BPS states of the N=4 type II compactification.

hep-th↗

arXiv2011

Generalized N=2 Topological Amplitudes and Holomorphic Anomaly Equation

In arXiv:0905.3629 we described a new class of N=2 topological amplitudes that depends both on vector and hypermultiplet moduli. Here we find that this class is actually a particular case of much more general topological amplitudes which appear at higher loops in heterotic string theory compactified on K3 x T^2. We analyze their effective field theory interpretation and derive particular (first order) differential equations as a consequence of supersymmetry Ward identities and the 1/2-BPS nature of the corresponding effective action terms. In string theory the latter get modified due to anomalous world-sheet boundary contributions, generalizing in a non-trivial way the familiar holomorphic and harmonicity anomalies studied in the past. We prove by direct computation that the subclass of topological amplitudes studied in arXiv:0905.3629 forms a closed set under these anomaly equations and that these equations are integrable.

hep-th↗

arXiv2010

N=4 Topological Amplitudes and Black Hole Entropy

We study the effects of N=4 topological string amplitudes on the entropy of black holes. We analyse the leading contribution associated to six-derivative terms and find one particular operator which can correct the entropy of N=4 black holes. This operator is BPS-like and appears in the effective action of type II string theory on K3 x T^2 or equivalently its heterotic dual on T^6. In both descriptions the leading contribution arises at one-loop, which we calculate explicitly on the heterotic side. We then consider whether this term has any consequences for the entropy of (large) N=4 black holes and find that it makes indeed a contribution at subleading order. Repeating the computation for small black holes with vanishing horizon area at the classical level, we prove that this coupling lifts certain flat directions in the entropy function thereby being responsible for the attractor equations of some moduli fields.

hep-th↗

arXiv2010

Deformed Topological Partition Function and Nekrasov Backgrounds

A deformation of the N=2 topological string partition function is analyzed by considering higher dimensional F-terms of the type W^{2g}*Upsilon^n, where W is the chiral Weyl superfield and each Upsilon factor stands for the chiral projection of a real function of N=2 vector multiplets. These terms generate physical amplitudes involving two anti-self-dual Riemann tensors, 2g-2 anti-self-dual graviphoton field strengths and 2n self-dual field strengths from the matter vector multiplets. Their coefficients F_{g,n} generalizing the genus g partition function F_{g,0} of the topological twisted type II theory, can be used to define a generating functional by introducing deformation parameters besides the string coupling. Choosing all matter field strengths to be that of the dual heterotic dilaton supermultiplet, one obtains two parameters that we argue should correspond to the deformation parameters of the Nekrasov partition function in the field theory limit, around the conifold singularity. Its perturbative part can be obtained from the one loop analysis on the heterotic side. This has been computed in [1] and in the field theory limit shown to be given by the radius deformation of c=1 CFT coupled to two-dimensional gravity. Quite remarkably this result reproduces the gauge theory answer up to a phase difference that may be attributed to the regularization procedure. The type II results are expected to be exact and should also capture the part that is non-perturbative in heterotic dilaton.

hep-th↗

arXiv2009

A New Class of N=2 Topological Amplitudes

We describe a new class of N=2 topological amplitudes that compute a particular class of BPS terms in the low energy effective supergravity action. Specifically they compute the coupling F^2(λλ)^{g-2}(dϕ)^2 where F, λand ϕare gauge field strengths, gaugino and holomorphic vector multiplet scalars. The novel feature of these terms is that they depend both on the vector and hypermultiplet moduli. The BPS nature of these terms implies that they satisfy a holomorphicity condition with respect to vector moduli and a harmonicity condition as well as a second order differential equation with respect to hypermultiplet moduli. We study these conditions explicitly in heterotic string theory and show that they are indeed satisfied up to anomalous boundary terms in the world-sheet moduli space. We also analyze the boundary terms in the holomorphicity and harmonicity equations at a generic point in the vector and hyper moduli space. In particular we show that the obstruction to the holomorphicity arises from the one loop threshold correction to the gauge couplings and we argue that this is due to the contribution of non-holomorphic couplings to the connected graphs via elimination of the auxiliary fields.

hep-th↗

arXiv2007

Harmonicity in N=4 supersymmetry and its quantum anomaly

The holomorphicity property of N=1 superpotentials or of N=2 F-terms involving vector multiplets is generalized to the case of N=4 1/2-BPS effective operators defined in harmonic superspace. The resulting harmonicity equations are shown to control the moduli dependence of the couplings of higher dimensional operators involving powers of the N=4 Weyl superfield, computed by N=4 topological amplitudes. These equations can also be derived on the string side, exhibiting an anomaly from world-sheet boundary contributions that leads to recursion relations for the non-analytic part of the couplings.

hep-th↗

arXiv2007

Topological Amplitudes and Physical Couplings in String Theory

In these lectures, we review the main properties of the topological theory obtained by twisting the N=2 two-dimensional superconformal algebra, associated to supersymmetric string compactifications. In particular, we describe a set of physical quantities in string theory that are computed by topological amplitudes. These are in general higher-dimensional F-terms in the low energy effective supergravity, or fermion masses after supersymmetry breaking. We discuss N=2 compactifications of type II strings, N=1 compactifications of heterotic and type I strings, as well as N=4 string vacua. Particular emphasis is put on alternative string dual representations allowing calculability, and on the generalization of N=2 holomorphicity and its anomaly.

hep-th↗

arXiv2006

N=4 Topological Amplitudes and String Effective Action

Certain scattering amplitudes in the gravitational sector of type II string theory on K3 x T^2 are found to be computed by correlation functions of the N=4 topological string. This analysis extends the already known results for K3 by Berkovits and Vafa, which correspond to six-dimensional terms in the effective action, involving four Riemann tensors and 4g-4 graviphotons, R^4T^{4g-4}, at genus g. We find two additional classes of topological amplitudes that use the full internal SCFT of K3 x T^2. One of these string amplitudes is mapped to a 1-loop contribution in the heterotic theory, and is studied explicitly. It corresponds to the four-dimensional term R^2(ddΦ)^2T^{2g-4}, with Φa Kaluza-Klein graviscalar from T^2. Finally, the generalization of the harmonicity relation for its moduli dependent coupling coefficient is obtained and shown to contain an anomaly, generalizing the holomorphic anomaly of the N=2 topological partition function F_g.

hep-th↗

arXiv2005

Divergences in Non-Commutative Gauge Theories with the Slavnov Term

The divergence structure of non-commutative gauge field theories (NCGFT) with a Slavnov extension is examined at one-loop level with main focus on the gauge boson self-energy. Using an interpolating gauge we show that even with this extension the quadratic IR divergence of the gauge boson self-energy is independent from a covariant gauge fixing as well as from an axial gauge. The proposal of Slavnov is based on the fact that the photon propagator shows a new transversality condition with respect to the IR dangerous terms. This novel transversality is implemented with the help of a new dynamical multiplier field. However, one expects that in physical observables such contributions disappear. A further new feature is the existence of new UV divergences compatible with the gauge invariance (BRST symmetry). We then examine two explicit models with couplings to fermions and scalar fields.

hep-th↗

arXiv2005

Gauge (in)dependence and UV/IR mixing

The gauge independence in connection with the UV/IR-mixing is discussed with the help of the non-commutative U(1)-gauge field model proposed by A. A. Slavnov with two different gauges: the covariant gauge fixing defined via a gauge parameter αand the non-standard axial-gauge depending on a fixed gauge direction n^μ.

hep-th↗