Searcharxiv⌕ Search

arXiv subjects

Yassen S. Stanev

Publications and source records attributed to Yassen S. Stanev.

18 recordsLinked to original sources
arXiv2013

Correlation functions of conserved currents in four dimensional conformal field theory with higher spin symmetry

We report some recent progress in the computation of the n-point correlation functions of conserved currents in a class of four dimensional conformal field theories with higher spin symmetry. Global conformal invariance leads to very strong constraints on both the general form and the singularity structure of the correlation functions of conserved currents. Namely, all these functions have to be rational functions with at most double pole singularities. We show that this implies that the 4-, 5- and 6-point correlation functions of the (symmetric, conserved and traceless) stress-energy tensor are linear combinations of the three free field expressions. Hence, in four dimensions, any globally conformal invariant theory is free.

hep-th↗
arXiv2013

Constraining conformal field theory with higher spin symmetry in four dimensions

We analyze the constraints on the general form and the singularity structure of the correlation functions of the symmetric, traceless and conserved stress-energy tensor implied by conformal invariance and higher spin symmetry in four dimensions. In particular, we show that all these correlation functions will have at most double pole singularities. We then compute the 4-, 5- and 6-point functions of the stress-energy tensor and find that they are linear combinations of the three free field expressions (scalar, fermion and Maxwell field). This is a strong indication that all such theories are essentially free.

hep-th↗
arXiv2012

Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory

We derive a generating function for all the 3-point functions of higher spin conserved currents in four dimensional conformal field theory. The resulting expressions have a rather surprising factorized form which suggest that they can all be realized by currents built from free massless fields of arbitrary (half-)integer spin s. This property is however not necessarily true also for the higher-point functions. As an illustration we analyze the general 4-point function of conserved abelian U(1) currents of scale dimension equal to three and find that apart from the two free field realizations there is a unique possible function which may correspond to an interacting theory. Although this function passes several non-trivial consistency tests, it remains an open challenging problem whether it can be actually realized in an interacting CFT.

hep-th↗
arXiv2008

Minimal Anomalous U(1)' Extension of the MSSM

We study an extension of the MSSM by an anomalous abelian vector multiplet and a Stückelberg multiplet. The anomalies are cancelled by the Green-Schwarz mechanism and the addition of Chern-Simons terms. The advantage of this choice over the standard one is that it allows for arbitrary values of the quantum numbers of the extra U(1). As a first step towards the study of hadron annihilations producing four leptons in the final state (a clean signal which might be studied at LHC) we then compute the decays $Z'\to Z_0 \g$ and $Z'\to Z_0 Z_0$. We find that the largest values of the decay rate is $\sim 10^{-4}$ GeV, while the expected number of events per year at LHC is at most of the order of 10.

hep-th↗
arXiv2007

On gauge couplings and thresholds in Type I Gepner models and otherwise

We derive general formulae for tree level gauge couplings and their one-loop thresholds in Type I models based on genuinely interacting internal N=2 SCFT's, such as Gepner models. We illustrate our procedure in the simple yet non-trivial instance of the Quintic. We briefly address the phenomenologically more relevant issue of determining the Weinberg angle in this class of models. Finally we initiate the study of the correspondence between `magnetized' or `coisotropic' D-branes in Gepner models and twisted representations of the underlying N=2 SCA.

hep-th↗
arXiv2005

Rationality of the Anomalous Dimensions in N=4 SYM theory

We reconsider the general constraints on the perturbative anomalous dimensions in conformal invariant QFT and in particular in N=4 SYM with gauge group SU(N_c). We show that all the perturbative corrections to the anomalous dimension of a renormalized gauge invariant local operator can be written as polynomials in its one loop anomalous dimension. In the N=4 SYM theory the coefficients of these polynomials are rational functions of the number of colours N_c.

hep-th↗
arXiv2003

Surprises from the Resolution of Operator Mixing in N = 4 SYM

We reexamine the problem of operator mixing in N = 4 SYM. Particular attention is paid to the correct definition of composite gauge invariant local operators, which is necessary for the computation of their anomalous dimensions beyond lowest order. As an application we reconsider the case of operators with naive dimension Delta_0=4, already studied in the literature. Stringent constraints from the resummation of logarithms in power behaviours are exploited and the role of the generalized N = 4 Konishi anomaly in the mixing with operators involving fermions is discussed. A general method for the explicit (numerical) resolution of the operator mixing and the computation of anomalous dimensions is proposed. We then resolve the order g^2 mixing for the 15 (purely scalar) singlet operators of naive dimension Δ_0=6. Rather surprisingly we find one isolated operator which has a vanishing anomalous dimension up to order g^4, belonging to an apparently long multiplet. We also solve the order g^2 mixing for the 26 operators belonging to the representation 20' of SU(4). We find an operator with the same one-loop anomalous dimension as the Konishi multiplet.

hep-th↗
arXiv2003

Globally conformal invariant gauge field theory with rational correlation functions

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_k (x_1, x_2) of dimension (k,k). For a {\it globally conformal invariant} (GCI) theory we write down the OPE of V_k into a series of {\it twist} (dimension minus rank) 2k symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field. We argue that the theory of a GCI hermitian scalar field L(x) of dimension 4 in D = 4 Minkowski space such that the 3-point functions of a pair of L's and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density L(x).

hep-th↗
arXiv2002

Global Conformal Invariance and Bilocal Fields with Rational Correlation Functions

The singular part of the \textit{operator product expansion} (OPE) of a pair of \textit{globally conformal invariant} (GCI) scalar fields $ϕ$ of (integer) dimension $d$ can be written as a sum of the 2-point function of $ϕ$ and $d-1$ bilocal conformal fields $V_ν(x_1, x_2)$ of dimension $(ν, ν)$, $ν= 1, ..., d-1$. As the correlation functions of $ϕ(x)$ are proven to be rational [6], we argue that the correlation functions of $V_ν$ can also be assumed rational. Each $V_ν(x_1, x_2)$ is expanded into local symmetric tensor fields of \textit{twist} (dimension minus rank) $2ν$. The case $d=2$, considered previously [5], is briefly reviewed and current work on the $d=4$ case (of a Lagrangean density in 4 space--time dimensions) is previewed.

hep-th↗
arXiv2002

On Operator Mixing in N=4 SYM

We resolve the mixing of the scalar operators of naive dimension 4 belonging to the representation 20' of the SU(4) R-symmetry in N=4 SYM. We compute the order g^2 corrections to their anomalous dimensions and show the absence of instantonic contributions thereof. Ratios of the resulting expressions are irrational numbers, even in the large N limit where, however, we observe the expected decoupling of double-trace operators from single-trace ones. We briefly comment on the generalizations of our results required in order to make contact with the double scaling limit of the theory conjectured to be holographically dual to type IIB superstring on a pp-wave.

hep-th↗
arXiv2002

Four Dimensional CFT Models with Rational Correlation Functions

Recently established rationality of correlation functions in a globally conformal invariant quantum field theory satisfying Wightman axioms is used to construct a family of soluble models in 4-dimensional Minkowski space-time. We consider in detail a model of a neutral scalar field $ϕ$ of dimension 2. It depends on a positive real parameter c, an analogue of the Virasoro central charge, and admits for all (finite) c an infinite number of conserved symmetric tensor currents. The operator product algebra of $ϕ$ is shown to coincide with a simpler one, generated by a bilocal scalar field $V(x_1,x_2)$ of dimension (1,1). The modes of V together with the unit operator span an infinite dimensional Lie algebra $L_V$ whose vacuum (i.e. zero energy lowest weight) representations only depend on the central charge c. Wightman positivity (i.e. unitarity of the representations of $L_V$) is proven to be equivalent to $c \in N$.

hep-th↗
arXiv2001

Properties of the Konishi multiplet in N=4 SYM theory

We study perturbative and non-perturbative properties of the Konishi multiplet in N=4 SYM theory in D=4 dimensions. We compute two-, three- and four-point Green functions with single and multiple insertions of the lowest component of the multiplet, and of the lowest component of the supercurrent multiplet. These computations require a proper definition of the renormalized operator and lead to an independent derivation of its anomalous dimension. The O(g^2) value found in this way is in agreement with previous results. We also find that instanton contributions to the above correlators vanish. From our results we are able to identify some of the lowest dimensional gauge-invariant composite operators contributing to the OPE of the correlation functions we have computed. We thus confirm the existence of an operator belonging to the representation 20', which has vanishing anomalous dimension at order g^2 and g^4 in perturbation theory as well as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions.

hep-th↗
arXiv1999

On the logarithmic behaviour in N=4 SYM theory

We show that the logarithmic behaviour seen in perturbative and non perturbative contributions to Green functions of gauge-invariant composite operators in N=4 SYM with SU(N) gauge group can be consistently interpreted in terms of anomalous dimensions of unprotected operators in long multiplets of the superconformal group SU(2,2|4). In order to illustrate the point we analyse the short-distance behaviour of a particularly simple four-point Green function of the lowest scalar components of the N=4 supercurrent multiplet. Assuming the validity of the Operator Product Expansion, we are able to reproduce the known value of the one-loop anomalous dimension of the single-trace operators in the Konishi supermultiplet. We also show that it does not receive any non-perturbative contribution from the one-instanton sector. We briefly comment on double- and multi-trace operators and on the bearing of our results on the AdS/SCFT correspondence.

hep-th↗
arXiv1997

Open Strings on the Neveu-Schwarz Pentabrane

We analyze the propagation of open and unoriented strings on the Neveu-Schwarz pentabrane (N5-brane) along the lines of a similar analysis for the SU(2) WZNW models. We discuss the two classes of open descendants of the diagonal models and a series of Z_2 projected models which exist only for even values of the level k and correspond to branes at D-type orbifold singularities. The resulting configurations of branes and planes are T-dual to those relevant to the study of dualities in super Yang-Mills theories. The association of Chan-Paton factors to D-brane multiplicities is possible in the semi-classical limit k -> infinity, but due to strong curvature effects is unclear for finite k. We show that the introduction of a magnetic field implies a twist of the SU(2) current algebra in the open-string sector leading to spacetime supersymmetry breaking.

hep-th↗
arXiv1996

Twelve-Dimensional Aspects of Four-Dimensional N=1 Type I Vacua

Four-dimensional supergravity theories are reinterpreted in a 12-dimensional F-theory framework. The O(8) symmetry of N=8 supergravity is related to a reduction of F-theory on T_8, with the seventy scalars formally associated, by O(8) triality, to a fully compactified four-form A_4. For the N=1 type I model recently obtained from the type IIB string on the Z orbifold, we identify the Kähler manifold of the untwisted scalars in the unoriented closed sector with the generalized Siegel upper-half plane Sp(8,R)/(SU(4) \times U(1)). The SU(4) factor reflects the holonomy group of Calabi-Yau fourfolds.

hep-th↗
arXiv1996

Open Descendants in Conformal Field Theory

Open descendants extend Conformal Field Theory to unoriented surfaces with boundaries. The construction rests on two types of generalizations of the fusion algebra. The first is needed even in the relatively simple case of diagonal models. It leads to a new tensor that satisfies the fusion algebra, but whose entries are signed integers. The second is needed when dealing with non-diagonal models, where Cardy's ansatz does not apply. It leads to a new tensor with positive integer entries, that satisfies a set of polynomial equations and encodes the classification of the allowed boundary operators.

hep-th↗
arXiv1996

Completeness Conditions for Boundary Operators in 2D Conformal Field Theory

In non-diagonal conformal models, the boundary fields are not directly related to the bulk spectrum. We illustrate some of their features by completing previous work of Lewellen on sewing constraints for conformal theories in the presence of boundaries. As a result, we include additional open sectors in the descendants of $D_{odd}$ $SU(2)$ WZW models. A new phenomenon emerges, the appearance of multiplicities and fixed-point ambiguities in the boundary algebra not inherited from the closed sector. We conclude by deriving a set of polynomial equations, similar to those satisfied by the fusion-rule coefficients $N_{ij}^k$, for a new tensor $A_{a b}^i$ that determines the open spectrum.

hep-th↗