Olaf Hohm
YOU?
Author Swipe
View article: Yang-Mills kinematic algebra via homotopy transfer from a worldline operator algebra
Yang-Mills kinematic algebra via homotopy transfer from a worldline operator algebra Open
The homotopy Lie or L ∞ algebra encoding Yang-Mills theory is the tensor product of a color Lie algebra with the kinematic C ∞ algebra. We derive this C ∞ algebra, via homotopy transfer, from a strict operator algebra of a worl…
View article: The double copy of maximal supersymmetry in D = 4
The double copy of maximal supersymmetry in D = 4 Open
A bstract We realize off-shell, local and gauge invariant $$ \mathcal{N} $$ = 8 supergravity in D = 4, to cubic order in fields, as the double copy of $$ \mathcal{N} $$ = 4 super Yang-Mills theory (SYM). Employing the homotopy algebra …
View article: Vertex operators for the kinematic algebra of Yang-Mills theory
Vertex operators for the kinematic algebra of Yang-Mills theory Open
The kinematic algebra of Yang-Mills theory can be understood in the framework of homotopy algebras: the L∞ algebra of Yang-Mills theory is the tensor product of the color Lie algebra and a kinematic space that carries a C∞ algebra. There a…
View article: The Double Copy of Maximal Supersymmetry in $D=4$
The Double Copy of Maximal Supersymmetry in $D=4$ Open
We realize off-shell, local and gauge invariant $N=8$ supergravity in $D=4$, to cubic order in fields, as the double copy of $N=4$ super Yang-Mills theory (SYM). Employing the homotopy algebra approach, we show that, thanks to a redundant …
View article: Off-Shell Quantum Mechanics as Factorization Algebras on Intervals
Off-Shell Quantum Mechanics as Factorization Algebras on Intervals Open
We present, for the harmonic oscillator and the spin-$\frac{1}{2}$ system, an alternative formulation of quantum mechanics that is `off-shell': it is based on classical off-shell configurations and thus similar to the path integral. The co…
View article: Holography as homotopy
Holography as homotopy Open
A bstract We give an interpretation of holography in the form of the AdS/CFT correspondence in terms of homotopy algebras. A field theory such as a bulk gravity theory can be viewed as a homotopy Lie or L ∞ algebra. We extend this dictiona…
View article: Vertex operators for the kinematic algebra of Yang-Mills theory
Vertex operators for the kinematic algebra of Yang-Mills theory Open
The kinematic algebra of Yang-Mills theory can be understood in the framework of homotopy algebras: the $L_{\infty}$ algebra of Yang-Mills theory is the tensor product of the color Lie algebra and a kinematic space that carries a $C_{\inft…
View article: Double copy of 3D Chern-Simons theory and 6D Kodaira-Spencer gravity
Double copy of 3D Chern-Simons theory and 6D Kodaira-Spencer gravity Open
We apply an algebraic double copy construction of gravity from gauge theory to three-dimensional (3D) Chern-Simons theory. The kinematic algebra K is the 3D de Rham complex of forms equipped, for a choice of metric, with a graded Lie algeb…
View article: Double Copy of 3D Chern-Simons Theory and 6D Kodaira-Spencer Gravity
Double Copy of 3D Chern-Simons Theory and 6D Kodaira-Spencer Gravity Open
We apply an algebraic double copy construction of gravity from gauge theory to three-dimensional (3D) Chern-Simons theory. The kinematic algebra ${\cal K}$ is the 3D de Rham complex of forms equipped, for a choice of metric, with a graded …
View article: Weakly constrained double field theory as the double copy of Yang-Mills theory
Weakly constrained double field theory as the double copy of Yang-Mills theory Open
The weakly constrained double field theory, in the sense of Hull and Zwiebach, captures the subsector of string theory on toroidal backgrounds that includes gravity, B-field, and dilaton together with all of their massive Kaluza-Klein and …
View article: Homological quantum mechanics
Homological quantum mechanics Open
A bstract We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of…
View article: Tree-level Scattering Amplitudes via Homotopy Transfer
Tree-level Scattering Amplitudes via Homotopy Transfer Open
We formalize the computation of tree-level scattering amplitudes in terms of the homotopy transfer of homotopy algebras, illustrating it with scalar $ϕ^3$ and Yang-Mills theory. The data of a (gauge) field theory with an action is encoded …
View article: Gravity = Yang–Mills
Gravity = Yang–Mills Open
This essay’s title is justified by discussing a class of Yang–Mills-type theories of which standard Yang–Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of homoto…
View article: Weakly Constrained Double Field Theory as the Double Copy of Yang-Mills Theory
Weakly Constrained Double Field Theory as the Double Copy of Yang-Mills Theory Open
Weakly constrained double field theory, in the sense of Hull and Zwiebach, captures the subsector of string theory on toroidal backgrounds that includes gravity, $B$-field and dilaton together with all of their massive Kaluza-Klein and win…
View article: On black hole singularity resolution in $D=2$ via duality-invariant $α'$ corrections
On black hole singularity resolution in $D=2$ via duality-invariant $α'$ corrections Open
Starting with the two-derivative limit of $D=2$ string theory, we explore the space of T-duality invariant $α'$ corrections, a space that contains a point representing the fully $α'$-corrected classical string theory. Using a parametrizati…
View article: Holography as Homotopy
Holography as Homotopy Open
We give an interpretation of holography in the form of the AdS/CFT correspondence in terms of homotopy algebras. A field theory such as a bulk gravity theory can be viewed as a homotopy Lie or $L_{\infty}$ algebra. We extend this dictionar…
View article: Gravity = Yang-Mills
Gravity = Yang-Mills Open
This essay's title is justified by discussing a class of Yang-Mills-type theories of which standard Yang-Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of homoto…
View article: Gauge invariant double copy of Yang-Mills theory: The quartic theory
Gauge invariant double copy of Yang-Mills theory: The quartic theory Open
We give an explicit gauge invariant, off-shell and local double copy construction of gravity from Yang-Mills theory to quartic order. To this end we use the framework of homotopy algebras, and we identify a rich new algebraic structure ass…
View article: Weakly constrained double field theory: the quartic theory
Weakly constrained double field theory: the quartic theory Open
Double field theory was originally introduced as the subsector of closed string field theory on a toroidal background given by the massless fields together with all their massive Kaluza-Klein and winding modes. These massive modes are enco…
View article: Cosmological Perturbations in Double Field Theory
Cosmological Perturbations in Double Field Theory Open
A bstract We explore perturbative double field theory about time-dependent (cosmological) backgrounds to cubic order. To this order the theory is consistent in a weakly constrained sense, so that for a toroidal geometry it encodes both mom…
View article: 2D Black Holes, Bianchi I Cosmologies, and $α'$
2D Black Holes, Bianchi I Cosmologies, and $α'$ Open
We report two surprising results on $α'$ corrections in string theory restricted to massless fields. First, for critical dimension Bianchi type I cosmologies with $q$ scale factors only $q-1$ of them have non-trivial $α'$ corrections. In p…
View article: Gauge invariant double copy of Yang-Mills theory: the quartic theory
Gauge invariant double copy of Yang-Mills theory: the quartic theory Open
We give an explicit gauge invariant, off-shell and local double copy construction of gravity from Yang-Mills theory to quartic order. To this end we use the framework of homotopy algebras, and we identify a rich new algebraic structure ass…
View article: U-duality and $\\alpha'$ corrections in three dimensions
U-duality and $\\alpha'$ corrections in three dimensions Open
We consider the target space theory of bosonic and heterotic string theory to\nfirst order in $\\alpha'$ compactified to three dimensions, using a formulation\nthat is manifestly T-duality invariant under ${\\rm O}(d,d,\\mathbb{R})$ with\n…
View article: U-duality and $α'$ corrections in three dimensions
U-duality and $α'$ corrections in three dimensions Open
We consider the target space theory of bosonic and heterotic string theory to first order in $α'$ compactified to three dimensions, using a formulation that is manifestly T-duality invariant under ${\rm O}(d,d,\mathbb{R})$ with $d=23$ and …
View article: An $α'$-complete theory of cosmology and its tensionless limit
An $α'$-complete theory of cosmology and its tensionless limit Open
We explore the exactly duality invariant higher-derivative extension of double field theory due to Hohm, Siegel and Zwiebach (HSZ) specialized to cosmological backgrounds. Despite featuring a finite number of derivatives in its original fo…
View article: Cosmological Perturbations in Double Field Theory
Cosmological Perturbations in Double Field Theory Open
We explore perturbative double field theory about time-dependent (cosmological) backgrounds to cubic order. To this order the theory is consistent in a weakly constrained sense, so that for a toroidal geometry it encodes both momentum and …
View article: The gauge structure of double field theory follows from Yang-Mills theory
The gauge structure of double field theory follows from Yang-Mills theory Open
We show that to cubic order double field theory is encoded in Yang-Mills theory. To this end we use algebraic structures from string field theory as follows: The $L_{\infty}$-algebra of Yang-Mills theory is the tensor product ${\cal K}\oti…
View article: Supersymmetric action for 6D $(4,0)$ supergravity
Supersymmetric action for 6D $(4,0)$ supergravity Open
We give a linearized but otherwise complete supersymmetric action for ${\cal N}=(4,0)$ supergravity in six dimensions, using a Kaluza-Klein-type $5+1$ split of coordinates and fields. We provide in particular a significantly simplified ver…
View article: Double field theory as the double copy of Yang-Mills theory
Double field theory as the double copy of Yang-Mills theory Open
We show that double field theory arises from the color-kinematic double copy of Yang-Mills theory. A precise double copy prescription for the Yang-Mills action at quadratic and cubic order is provided that yields the double field theory ac…