Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHomotopy Transfer and Effective Field Theory I: Tree-level
76
0
0.0
(
0
)
Added by
Alexandros Spyridon Arvanitakis
Publication date
2020
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We use the dictionary between general field theories and strongly homotopy algebras to provide an algebraic formulation of the procedure of integrating out of degrees of freedom in terms of homotopy transfer. This includes more general effective theories in which some massive modes are kept while other modes of a comparable mass scale are integrated out, as first explored by Sen in the context of closed string field theory. We treat $L_infty$-algebras both in terms of a nilpotent coderivation and, on the dual space, in terms of a nilpotent derivation (corresponding to the BRST charge of the field theory) and provide explicit formulas for homotopy transfer. These are then shown to govern the integrating out of degrees of freedom at tree level, while the generalization to loop level will be explored in a sequel to this paper.
rate research
Read More
We continue our study of effective field theory via homotopy transfer of $L_infty$-algebras, and apply it to tree-level non-Wilsonian effective actions of the kind discussed by Sen in which the modes integrated out are comparable in mass to the modes that are kept. We focus on the construction of effective actions for string states at fixed levels and in particular on the construction of weakly constrained double field theory. With these examples in mind, we discuss closed string theory on toroidal backgrounds and resolve some subtle issues involving vertex operators, including the proper form of cocycle factors and of the reflector state. This resolves outstanding issues concerning the construction of covariant closed string field theory on toroidal backgrounds. The weakly constrained double field theory is formally obtained from closed string field theory on a toroidal background by integrating out all but the doubly massless states and homotopy transfer then gives a prescription for determining the theorys vertices and symmetries. We also discuss consistent truncation in the context of homotopy transfer.
We show that the tree-level S-matrices of the superstring field theories based on the homotopy-algebra structure agree with those obtained in the first-quantized formulation. The proof is given in detail for the heterotic string field theory. The extensions to the type II and open superstring field theories are straightforward.
By the use of cyclic symmetry, KK relations and BCJ relations, one can reduce the number of independent $N$-point color-ordered tree amplitudes in gauge theory and string theory from $N!$ to $(N-3)!$. In this paper, we investigate these relations at tree-level in both string theory and field theory. We will show that there are two primary relations. All other relations can be generated by the primary relations. In string theory, the primary relations can be chosen as cyclic symmetry as well as either the fundamental KK relation or the fundamental BCJ relation. In field theory, the primary relations can only be chosen as cyclic symmetry and the fundamental BCJ relation. We will further show a kind of more general relation which can also be generated by the primary relations. The general formula of the explicit minimal-basis expansions for color-ordered open string tree amplitudes will be given and proven in this paper.
Pair creation of strings in time-dependent backgrounds is studied from an effective field theory viewpoint, and some possible cosmological applications are discussed. Simple estimates suggest that excited strings may have played a significant role in preheating, if the string tension as measured in four-dimensional Einstein frame falls a couple of orders of magnitude below the four-dimensional Planck scale.
We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory. This is illustrated for Yang-Mills theory, gravity on flat and cosmological backgrounds and for the massless sector of closed string theory. The perturbation lemma yields an algorithmic procedure to determine the higher corrections of the gauge invariant variables and the action in terms of these.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
