Ultraviolet structure of half-maximal supergravity with matter multiplets at two and three loops

TY - JOUR

T1 - Ultraviolet structure of half-maximal supergravity with matter multiplets at two and three loops

AU - Bern, Zvi

AU - Davies, Scott

AU - Dennen, Tristan Lucas

PY - 2013/9/5

Y1 - 2013/9/5

N2 - Using the duality between color and kinematics, we construct the two- and three-loop amplitudes of half-maximal supergravity with matter multiplets and show that new divergences occur in D=4 and D=5. In a recent paper, Bossard, Howe and Stelle conjecture the existence of 16-supercharge off-shell harmonic superspaces in order to explain the ultraviolet finiteness of pure half-maximal supergravity with no matter multiplets in D=4 at three loops and in D=5 at two loops. By assuming the required superspace exists in D=5, they argue that no new divergences should occur at two loops even with the addition of Abelian-vector matter multiplets. Up to possible issues with the SL(2,R) global anomaly of the theory, they reach a similar conclusion in D=4 for two and three loops. The divergences we find contradict these predictions based on the existence of the desired off-shell superspaces. Furthermore, our D=4 results are incompatible with the new divergences being due to the anomaly. We find that the two-loop divergences of half-maximal supergravity are directly controlled by the divergences appearing in ordinary nonsupersymmetric Yang-Mills theory coupled to scalars, explaining why half-maximal supergravity develops new divergences when matter multiplets are added. We also provide a list of one- and two-loop counterterms that should be helpful for constraining any future potential explanations of the observed vanishings of divergences in pure half-maximal supergravity.

AB - Using the duality between color and kinematics, we construct the two- and three-loop amplitudes of half-maximal supergravity with matter multiplets and show that new divergences occur in D=4 and D=5. In a recent paper, Bossard, Howe and Stelle conjecture the existence of 16-supercharge off-shell harmonic superspaces in order to explain the ultraviolet finiteness of pure half-maximal supergravity with no matter multiplets in D=4 at three loops and in D=5 at two loops. By assuming the required superspace exists in D=5, they argue that no new divergences should occur at two loops even with the addition of Abelian-vector matter multiplets. Up to possible issues with the SL(2,R) global anomaly of the theory, they reach a similar conclusion in D=4 for two and three loops. The divergences we find contradict these predictions based on the existence of the desired off-shell superspaces. Furthermore, our D=4 results are incompatible with the new divergences being due to the anomaly. We find that the two-loop divergences of half-maximal supergravity are directly controlled by the divergences appearing in ordinary nonsupersymmetric Yang-Mills theory coupled to scalars, explaining why half-maximal supergravity develops new divergences when matter multiplets are added. We also provide a list of one- and two-loop counterterms that should be helpful for constraining any future potential explanations of the observed vanishings of divergences in pure half-maximal supergravity.

U2 - 10.1103/PhysRevD.88.065007

DO - 10.1103/PhysRevD.88.065007

M3 - Journal article

SN - 2470-0010

VL - 88

JO - Physical Review D

JF - Physical Review D

IS - 6

M1 - 065007

ER -