Supersymmetric virtual effects in heavy quark pair production at LHC

We consider the production of heavy ($b,t$) quark pairs at proton colliders in the theoretical framework of the MSSM. Under the assumption of a "moderately" light SUSY scenario, we first compute the leading logarithmic MSSM contributions at one loop for the elementary processes of production from a quark and from a gluon pair in the 1 TeV c.m. energy region. We show that in the initial gluon pair case (dominant in the chosen situation at LHC energies) the electroweak and the strong SUSY contributions concur to produce an enhanced effect whose relative value in the cross sections could reach the twenty percent size for large $\tan\beta$ values in the realistic proton-proton LHC process.Comment: 19 pages and 8 figures; version to appear in Phys. Rev.

Conformal a-anomaly of some non-unitary 6d superconformal theories

We compute the conformal anomaly a-coefficient for some non-unitary (higher derivative or non-gauge-invariant) 6d conformal fields and their supermultiplets. We use the method based on a connection between 6d determinants on S^6 and 7d determinants on AdS_7. We find, in particular, that (1,0) supermultiplet containing 4-derivative gauge-invariant conformal vector has precisely the value of a-anomaly as attributed in arXiv:1506.03807 (on the basis of R-symmetry and gravitational 't Hooft matching) to the standard (1,0) vector multiplet. We also show that higher derivative (2,0) 6d conformal supergravity coupled to exactly 26 (2,0) tensor multiplets has vanishing a-anomaly. This is the 6d counterpart of the known fact of cancellation of the conformal anomaly in the 4d system of N=4 conformal supergravity coupled to 4 vector N=4 multiplets. In the case when 5 of tensor multiplets are chosen to be ghost-like and the conformal symmetry is spontaneously broken by a quadratic scalar constraint the resulting IR theory may be identified with (2,0) Poincare supergravity coupled to 21=26-5 tensor multiplets. The latter theory is known to be special: it is gravitational anomaly free and results upon compactification of 10d type IIB supergravity on K3.Comment: 22 pages. v3: minor comments and references added, appendix expanded; v4: minor correction

Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT

We consider general-symmetry higher spin fields in AdS_5 and derive expressions for their one-loop corrections to vacuum energy E and the associated 4d boundary conformal anomaly a-coefficient. We a propose a similar expression for the second conformal anomaly c-coefficient. We show that all the three quantities (E, a, c) computed for N=8 gauged 5d supergravity are -1/2 of the values for N=4 conformal 4d supergravity and also twice the values for N=4 Maxwell multiplet. This gives 5d derivation of the fact that the system of N=4 conformal supergravity and four N=4 Maxwell multiplets is anomaly free. The values of (E, a, c) for the states at level p of Kaluza-Klein tower of 10d type IIB supergravity compactified on S^5 turn out to be equal to those for p copies of N=4 Maxwell multiplets. This may be related to the fact that these states appear in the tensor product of p superdoubletons. Under a natural regularization of the sum over p, the full 10d supergravity contribution is then minus that of the Maxwell multiplet, in agreement with the standard adjoint AdS/CFT duality (SU(n) SYM contribution is n^2-1 of one Maxwell multiplet). We also verify the matching of (E, a, c) for spin 0 and 1/2 boundary theory cases of vectorial AdS/CFT duality. The consistency conditions for vectorial AdS/CFT turn out to be equivalent to the cancellation of anomalies in the closely related 4d conformal higher spin theories. In addition, we study novel example of vectorial AdS/CFT duality when the boundary theory is described by free spin 1 fields and is dual to a particular higher spin theory in AdS_5 containing fields in mixed-symmetry representations. We also discuss its supersymmetric generalizations.Comment: 56 pages. v2,v3: minor corrections, references adde

On higher spin partition functions

We observe that the partition function of the set of all free massless higher spins s=0,1,2,3,... in flat space is equal to one: the ghost determinants cancel against the "physical" ones or, equivalently, the (regularized) total number of degrees of freedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z=1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z=1 is also true in the conformal higher spin theory (with higher-derivative d^{2s} kinetic terms) expanded near flat or conformally flat S^4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat 4d space. This non-unitary theory has a Weyl-invariant action in curved background and corresponds to "partially massless" field in AdS_5. We discuss in detail the special case of s=2 (or "conformal graviton"), compute the corresponding conformal anomaly coefficients and compare them with previously found expressions for generic representations of conformal group in 4 dimensions.Comment: 35 pages. v3: minor clarifications, comments, and references adde

Two-loop electroweak corrections at high energies

We discuss two-loop leading and angular-dependent next-to-leading logarithmic electroweak virtual corrections to arbitrary processes at energies above the electroweak scale. The relevant Feynman diagrams involving soft-collinear gauge bosons gamma, Z, W, have been evaluated in eikonal approximation. We present results obtained from the analytic evaluation of massive loop integrals. To isolate mass singularities we used the Sudakov method and alternatively the sector decomposition method in the Feynman-parameter representation.Comment: 5 pages. Talk presented by S.P. at the International Symposium on Radiative Corrections RADCOR 2002, September 8-13, Kloster Banz, Germany. To appear in the proceeding

Conformal anomaly c-coefficients of superconformal 6d theories

We propose general relations between the conformal anomaly and the chiral (R-symmetry and gravitational) anomaly coefficients in 6d (1,0) superconformal theories. The suggested expressions for the three type B conformal anomaly c-coefficients complement the expression for the type A anomaly a-coefficient found in arXiv:1506.03807. We check them on several examples -- the standard (1,0) hyper and tensor multiplets as well as some higher derivative short multiplets containing vector fields that generalize the superconformal 6d vector multiplet discussed in arXiv:1506.08727. We also consider a family of higher derivative superconformal (2,0) 6d multiplets associated to 7d multiplets in the KK spectrum of 11d supergravity compactified on S^4. In particular, we prove that (2,0) 6d conformal supergravity coupled to 26 tensor multiplets is free of all chiral and conformal anomalies. We discuss some interacting (1,0) superconformal theories, predicting the c-coefficients for the "E-string" theory on multiple M5-branes at E_8 9-brane and for the theory describing M5-branes at an orbifold singularity. Finally, we elaborate on holographic computation of subleading corrections to conformal anomaly coefficients coming from R^2+R^3 terms in 7d effective action, revisiting, in particular, the (2,0) theory case.Comment: 32 pages, v4: Added footnotes 8, 25, 26 clarifying that the available data leads to a 1-parameter family of the conformal anomaly coefficients c_1, c_2 as functions of chiral anomaly coefficients; the results for c_i in recent arXiv:1702.03518 also belong to this famil

On boundary correlators in Liouville theory on AdS2_{2}

We consider the Liouville theory in fixed Euclidean AdS$_2$ background. Expanded near the minimum of the potential the elementary field has mass squared 2 and (assuming the standard Dirichlet b.c.) corresponds to a dimension 2 operator at the boundary. We provide strong evidence for the conjecture that the boundary correlators of the Liouville field are the same as the correlators of the holomorphic stress tensor (or the Virasoro generator with the same central charge) on a half-plane or a disc restricted to the boundary. This relation was first observed at the leading semiclassical order (tree-level Witten diagrams in AdS$_2$) in arXiv:1902.10536 and here we demonstrate its validity also at the one-loop level. We also discuss arguments that may lead to its general proof.Comment: 23 pages, 1 pdf figure. v2: minor change

CTC_T for conformal higher spin fields from partition function on conically deformed sphere

We consider the one-parameter generalization $S^4_q$ of 4-sphere with a conical singularity due to identification $\tau=\tau + 2 \pi q$ in one isometric angle. We compute the value of the spectral zeta-function at zero $z(q) = \zeta(0, q)$ that controls the coefficient of the logarithmic UV divergence of the one-loop partition function on $S^4_q$. While the value of the conformal anomaly a-coefficient is proportional to $z(1)$, we argue that in general the second $c = C_T$ anomaly coefficient is related to a particular combination of the second and first derivatives of $z(q)$ at $q=1$. The universality of this relation for $C_T$ is supported also by examples in 6 and 2 dimensions. We use it to compute the c-coefficient for conformal higher spins finding that it coincides with the "$r=-1$" value of the one-parameter Ansatz suggested in arXiv:1309.0785. Like the sums of $a_s$ and $c_s$ coefficients, the regularized sum of $z_s(q)$ over the whole tower of conformal higher spins $s=1,2, ...$ is found to vanish, implying UV finiteness on $S^4_q$ and thus also the vanishing of the associated Re'nyi entropy. Similar conclusions are found to apply to the standard 2-derivative massless higher spin tower. We also present an independent computation of the full set of conformal anomaly coefficients of the 6d Weyl graviton theory defined by a particular combination of the three 6d Weyl invariants that has a (2,0) supersymmetric extension.Comment: 29 pages. v2: minor change

Charged Higgs Production in the 1 TeV Domain as a Probe of Supersymmetric Models

We consider the production, at future lepton colliders, of charged Higgs pairs in supersymmetric models. Assuming a relatively light SUSY scenario, and working in the MSSM, we show that, for c.m. energies in the one TeV range, a one-loop logarithmic Sudakov expansion that includes an "effective" next-to subleading order term is adequate to the expected level of experimental accuracy. We consider then the coefficient of the linear (subleading) SUSY Sudakov logarithm and the SUSY next to subleading term of the expansion and show that their dependence on the supersymmetric parameters of the model is drastically different. In particular the coefficient of the SUSY logarithm is only dependent on $\tan\beta$ while the next to subleading term depends on a larger set of SUSY parameters. This would allow to extract from the data separate informations and tests of the model.Comment: 18 pages and 13 figures e-mail: [email protected]

Two-loop electroweak angular-dependent logarithms at high energies

We present results on the two-loop leading and angular-dependent next-to-leading logarithmic virtual corrections to arbitrary processes at energies above the electroweak scale. In the `t Hooft-Feynman gauge the relevant Feynman diagrams involving soft and collinear gauge bosons \gamma, Z, W^\pm coupling to external legs are evaluated in the eikonal approximation in the region where all kinematical invariants are much larger than the electroweak scale. The logarithmic mass singularities are extracted from massive multi-scale loop integrals using the Sudakov method and alternatively the sector-decomposition method in the Feynman-parameter representation. The derivations are performed within the spontaneously broken phase of the electroweak theory, and the two-loop results are in agreement with the exponentiation prescriptions that have been proposed in the literature based on a symmetric SU(2) x U(1) theory matched with QED at the electroweak scale.Comment: 31 pages, LaTe