1,721,009 research outputs found
The D-2k R-4 invariants of N=8 supergravity
Get PDFThe existence of a linearized SUSY invariant for N=8 supergravity whose gravitational components are usually called R[superscript 4] was established long ago by on-shell super-space arguments. Superspace and string theory methods have also established analogous higher dimensional D[superscript 2k] R[superscript 4] invariants. However, very little is known about the SUSY completions of these operators which involve other fields of the theory. In this paper we find the detailed component expansion of the linearized R[superscript 4] invariant starting from the corresponding superamplitude which generates all component matrix elements of the operator. It is then quite straightforward to extend results to the entire set of D[superscript 2k] R[superscript 4] operators.Istituto nazionale di fisica nucleare (INFN) (Bruno Rossi fellowship)National Science Foundation (U.S.) (grant PHY-0967299)United States. Dept. of Energy (cooperative research agreement DE-FG02-05ER41360
Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
No full textWe prove that 1-loop n-point NMHV superamplitudes in N=4 SYM theory are dual conformal covariant for all numbers n of external particles (after regularization and subtraction of IR divergences). This property was previously established for n ≤ 9 in arXiv:0808.0491. We derive an explicit representation of these superamplitudes in terms of dual conformal cross-ratios. We also show that all the 1-loop ‘box coefficients’ obtained from maximal cuts of N k MHV n-point functions are covariant under dual conformal transformations.MIT-France Seed FundFrance. Commissariat à l'énergie atomique. Saclay LaboratoryNiels Bohr International AcademyNational Science Foundation (U.S.) (grant PHY-0503584)National Science Foundation (U.S.) (grant PHY-0600465)United States. Dept. of Energy (cooperative research agreement DE-FG0205ER41360
Recursion relations, generating functions, and unitarity sums in N=4 SYM theory
No full textWe prove that the MHV vertex expansion is valid for any NMHV tree amplitude of Script N = 4 SYM. The proof uses induction to show that there always exists a complex deformation of three external momenta such that the amplitude falls off at least as fast as 1/z for large z. This validates the generating function for n-point NMHV tree amplitudes. We also develop generating functions for anti-MHV and anti-NMHV amplitudes. As an application, we use these generating functions to evaluate several examples of intermediate state sums on unitarity cuts of 1-, 2-, 3- and 4-loop amplitudes. In a separate analysis, we extend the recent results of arXiv:0808.0504 to prove that there exists a valid 2-line shift for any n-point tree amplitude of Script N = 4 SYM. This implies that there is a BCFW recursion relation for any tree amplitude of the theory
SUSY Ward identities, superamplitudes and counterterms
Get PDFWard identities of SUSY and R-symmetry relate n -point amplitudes in supersymmetric theories. We review recent work in which these Ward identities are solved in ##IMG## [http://ej.iop.org/images/1751-8121/44/45/454009/jpa389327ieqn1.gif] {{\cal N}=4} SYM and ##IMG## [http://ej.iop.org/images/1751-8121/44/45/454009/jpa389327ieqn2.gif] {{\cal N}=8} supergravity. The solution, valid at both tree and loop level, expresses any N K MHV superamplitude in terms of a basis of ordinary amplitudes. Basis amplitudes are classified by semi-standard tableaux of rectangular ##IMG## [http://ej.iop.org/images/1751-8121/44/45/454009/jpa389327ieqn3.gif] {{\cal N}} _ K Young diagrams. The SUSY Ward identities also impose constraints on the matrix elements of candidate ultraviolet counterterms in ##IMG## [http://ej.iop.org/images/1751-8121/44/45/454009/jpa389327ieqn4.gif] {{\cal N}=8} supergravity, and they can be studied using superamplitude basis expansions. This leads to a novel and quite comprehensive matrix element approach to counterterms, which we also review.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90831/1/1751-8121_44_45_454009.pd
Off-shell Poincaré supergravity
Get PDFWe present the action and transformation rules of Poincaré supergravity coupled to chiral multiplets (z[superscript α], χ[superscript α], h[superscript α] ) with off-shell auxiliary fields. Starting from the geometric formulation of the superconformal theory with auxiliary fields, we derive the Poincaré counterpart by gauge-fixing the Weyl and chiral symmetry and S-supersymmetry. We show how this transition is facilitated by retaining explicit target-space covariance. Our results form a convenient starting point to study models with constrained superfields, including general matter-coupled de Sitter supergravity. Keywords: Supergravity Models, Supersymmetric Effective Theories, Supersymmetry
BreakingNational Science Foundation (U.S.) (Grant PHY-1620045
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The holography of F -maximization
Get PDFWe find new supersymmetric backgrounds of N = 8 gauged supergravity in four Euclidean dimensions that are dual to deformations of ABJM theory on S 3. The deformations encode the most general choice of U(1) R symmetry used to define the theory on S 3. We work within an N = 2 truncation of the N = 8 supergravity theory obtained via a group theory argument. We find perfect agreement between the S 3 free energy computed from our supergravity backgrounds and the previous field theory computations of the same quantity based on supersymmetric localization and matrix model techniques
TT¯ -deformed actions and (1,1) supersymmetry
Get PDFWe describe an algorithmic method to calculate the TT¯ deformed Lagrangian of a given seed theory by solving an algebraic system of equations. This method is derived from the topological gravity formulation of the deformation. This algorithm is far simpler than the direct partial differential equations needed in most earlier proposals. We present several examples, including the deformed Lagrangian of (1,1) supersymmetry. We show that this Lagrangian is off-shell invariant through order λ2 in the deformation parameter and verify its SUSY algebra through order λ.Fil: Coleman, Evan Austen. University of Stanford. Physics Department; Estados UnidosFil: Aguilera Damia, Jeremías. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Freedman, Daniel Z.. University of Stanford. Physics Department; Estados Unidos. Massachusetts Institute of Technology; Estados UnidosFil: Soni, Ronak M.. University of Stanford. Physics Department; Estados Unido
A simple approach to counterterms in N=8 supergravity
Get PDFWe present a simple systematic method to study candidate counterterms in =8 supergravity. Complicated details of the counterterm operators are avoided because we work with the on-shell matrix elements they produce. All n-point matrix elements of an independent SUSY invariant operator of the form D 2k R n+... must be local and satisfy SUSY Ward identities. These are strong constraints, and we test directly whether or not matrix elements with these properties can be constructed. If not, then the operator does not have a supersymmetrization, and it is excluded as a potential counterterm. For n> 4, we find that R n, D 2 R n, D 4 R n, and D 6 R n are excluded as counterterms of MHV amplitudes, while only R n and D 2 R n are excluded at the NMHV level. As a consequence, for loop order L4. If an operator is not ruled out, our method constructs an explicit superamplitude for its matrix elements. This is done for the 7-loop D 4 R 6 operator at the NMHV level and in other cases. We also initiate the study of counterterms without leading pure-graviton matrix elements, which can occur beyond the MHV level. The landscape of excluded/ allowed candidate counterterms is summarized in a colorful chart.United States. Dept. of Energy (grant DE-FG02- 95ER40899 )National Science Foundation (U.S.) (NSF grant PHY-0503584)National Science Foundation (U.S.) (grant No. PHY-0600465)United States. Dept. of Energy (cooperative research agreement DE-FG-0205FR41360)National Science Foundation (U.S.) (NSF grant PHY-0756966
Explicitly broken supersymmetry with exactly massless moduli
No full textThe AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a super-gravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents
Solution to the Ward identities for superamplitudes
No full textSupersymmetry and R-symmetry Ward identities relate on-shell amplitudes in a supersymmetric field theory. We solve these Ward identities for N [superscript K] MHV amplitudes of the maximally supersymmetric =4 and =8 theories. The resulting superamplitude is written in a new, manifestly supersymmetric and [subscript R]-invariant form: it is expressed as a sum of very simple SUSY and SUR -invariant Grassmann polynomials, each multiplied by a “basis amplitude”. For N [superscript K] MHV n-point superamplitudes the number of basis amplitudes is equal to the dimension of the irreducible representation of SU(n − 4) corresponding to the rectangular Young diagram with columns and K rows. The linearly independent amplitudes in this algebraic basis may still be functionally related by permutation of momenta. We show how cyclic and reflection symmetries can be used to obtain a smaller functional basis of color-ordered single-trace amplitudes in =4 gauge theory. We also analyze the more significant reduction that occurs in =8 supergravity because gravity amplitudes are not ordered. All results are valid at both tree and loop level
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