2017/08/31 by A. A. Tseytlin, A A Tseytlin · 8 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal anomaly #Conformal map #Dimension (graph theory) #Gauge theory #Graviton #Higher-dimensional supergravity #Holomorphic function #Kinetic term #Noncommutative and Quantum Gravity Theories #Quantum Chromodynamics and Particle Interactions #Scalar (mathematics) #Supergravity #hep-th
paper · pdf · doi:10.1088/1751-8121/aa920d
published in Journal of Physics A Mathematical and Theoretical 50(48), 48LT01 (Institute of Physics) · 6 pages. v2: minor comment and references added
arxiv created 2017/09/04 · openalex created_date 2017/09/15 · openalex publication_date 2017/10/09 · arxiv updated 2017/11/22 · openalex updated_date 2026/08/05
Abstract We review the question of quantum consistency of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mstyle> </mml:math> conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard (‘minimal’) conformal supergravity where the complex scalar <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>φ</mml:mi> </mml:mstyle> </mml:math> is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mstyle> </mml:math> super Yang–Mills with gauge group of dimension 4. The same turns out to be true also for the ‘non-minimal’ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mstyle> </mml:math> conformal supergravity with the action (recently constructed (Butter et al 2017 Phys. Rev. Lett . 118 081602)) depending on an arbitrary holomorphic function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>φ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> . The special case of the ‘non-minimal’ conformal supergravity with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>f</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>φ</mml:mi> </mml:mrow> </mml:msup> </mml:mstyle> </mml:math> appears in the twistor-string theory. We show that divergences and anomalies do not depend on the form of the function f and thus can be cancelled just as in the ‘minimal’ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>f</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mstyle> </mml:math> case by coupling the theory to four <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mstyle> </mml:math> vector multiplets.