Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

Abstract

Using the duality between color and kinematics, we construct two-loop fourpoint scattering amplitudes in N = 2 super-Yang-Mills (SYM) theory coupled to N f fundamental hypermultiplets. Our results are valid in D ≤ 6 dimensions, where the upper bound corresponds to six-dimensional chiral N = (1, 0) SYM theory. By exploiting a close connection with N = 4 SYM theory -and, equivalently, six-dimensional N = (1, 1) SYM theory -we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding D-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning N f enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in D = 4. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with N = (1, 1) and N = (2, 0) supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in D = 5 − 2 and show that it non-trivially cancels out as expected.

Gauged Supergravities and Spontaneous Supersymmetry Breaking from the Double Copy Construction

“…[10,11]. The double copy applies to tree-and loop-level amplitudes [12][13][14], as well as classical solutions [15][16][17], and extends earlier string-theory results [18]. Recent success in reformulating large families of Maxwell-Einstein (ME) [19][20][21][22][23] and Yang-Mills-Einstein (YME) supergravities [24][25][26] in the double copy language has prompted the proposal that all theories of gravity could be regarded as double copies of some sort [22] (see also [27]).…”

Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

“…We discuss in more detail the N = 2 SQCD theory, whose amplitudes we study in this paper. The theory is built from N = 2 SYM coupled to N f supersymmetric quarks transforming under the fundamental representation of the gauge group G. One can view it as a two-fold supersymmetry enhancement of QCD, or as an orbifold truncation of N = 4 SYM [76][77][78][79][80], where half of the particle content is promoted to the fundamental or antifundamental representation of the gauge group [44]. In Table 1 we summarize its particle-helicity content while displaying its intermediate position between the physical theory of massless QCD and the maximally supersymmetric N = 4 SYM theory (in which no matter content is permitted).…”

Five-loop four-point integrand of N=8 supergravity as a generalized double copy

“…where we have suppressed overall factors of the (κ/2) gravitational coupling and 32) and we used the factorization of the state sums as in Eq. (2.27).…”

“…(3.19) with the matrix σ; since σ · n BCJ = 0 and further using Eq. (3.28) we are left with 32) where as before α independent is the vector of independent functions specifying the generalized gauge parameters. This is closely related to the discussion in Ref.…”

“…At loop level the duality has conjectural status, supported by case-by-case explicit calculations. The duality has been crucial in the construction of numerous gravity multiloop amplitudes [4,11,31,32], where it has been used to identify new nontrivial ultraviolet cancellations in N = 4 and N = 5 supergravity [13,15], known as 'enhanced cancellations'. Apart from offering a simple means for obtaining loop-level scattering amplitudes in a multitude of (super)gravity theories, the duality also addresses the construction of black-hole and other classical solutions [33] including those potentially relevant to gravitational-wave observations [34], corrections to gravitational potentials [35], the relation between supergravity symmetries and gauge-theory ones [20,22,36], and the construction of multiloop form factors [37].…”