arXiv subjects

John H. Schwarz

Publications and source records attributed to John H. Schwarz.

At least 19 recordsLinked to original sources

arXiv2024

From Hadrons to Gravitons via Strings

The first quantum string theories were developed around 1970, prior to the discovery of QCD, with the goal of producing a theory of hadrons. Basic physical requirements and mathematical consistency of the string theories known at that time turned out to require the inclusion of gravity and the existence of extra spatial dimensions. This came as a complete surprise to everyone who was involved. It led to a completely new and very ambitious goal for string theory research, namely a unified quantum theory of gravity and all other forces. In particular, this goal requires that the string tension is 20 orders of magnitude larger than was previously envisioned. Fifty years later, this goal is widely shared.

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arXiv2024

Comments Concerning a Hypothetical Mesoscopic Dark Dimension

Motivated by string-theoretic swampland conjectures, the existence of a dark fifth dimension, whose size is roughly 1 -- 10 microns, has been proposed. A great deal of supporting evidence has been presented, and definitive experimental tests are likely to be carried out. The basic idea is that the four-dimensional spacetime that we observe lives on a brane that is localized in the dark dimension. This short note points out that there are two distinct ways to realize such a scenario in string theory/M-theory. In the one considered previously the dark dimension is topologically a circle and our observable 4d spacetime is confined to a brane that is localized in a GUT-scale region of the circle. An alternative possibility is that the dark dimension is a line interval with branes attached at each end. This option would imply the existence of a parallel 4d spacetime microns away from us!

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arXiv2022

Diffeomorphism Symmetry in Two Dimensions and Celestial Holography

Two-dimensional diffeomorphism symmetry can be described by an operator algebra extension of the well-known Virasoro algebra description of conformal symmetry. Utilizing this extension, this note explains why the conformal symmetry that appears in celestial holography should not be extended to diffeomorphism symmetry, a possibility that several authors have proposed. The description of the two-dimensional diffeomorphism algebra presented here might be useful for other purposes.

hep-th↗

arXiv2020

The $\mathbf{AdS_5 \times S^5}$ Superstring

The duality between the type IIB superstring theory in an $AdS_5 \times S^5$ background with $N$ units of five-form flux and ${\cal N} =4$ super Yang--Mills theory with a $U(N)$ gauge group has been studied extensively. My version of the construction of the superstring world-sheet action is reviewed here. This paper is dedicated to Michael Duff on the occasion of his 70th birthday.

hep-th↗

arXiv2020

M5-Brane Amplitudes

The dynamics of a probe M5-brane, embedded as a hypersurface in eleven-dimensional Minkowski spacetime, is described by a six-dimensional world-volume theory. This theory has a variety of interesting symmetries some of which are obscure in the Lagrangian formulation of the theory. However, as summarized in this review, an alternative approach is to construct all of its on-shell tree-level scattering amplitudes. This enables understanding all of the symmetries in a satisfying way. This work is dedicated to the memory of Peter Freund.

hep-th↗

arXiv2019

Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian

Recently, twistor-like formulations of tree amplitudes involving $n$ massless particles have been proposed for various 6D supersymmetric theories. The formulas are based on two different forms of the scattering equations: one based on rational maps and the other based on polarized scattering equations. We show that both formulations can be interpreted in terms of a symplectic (or complex Lagrangian) Grassmannian, $\mathbb{LG}(n, 2n)$, and that they correspond to different ways of fixing the ${\rm GL}(n, \mathbb{C})$ symmetry of $\mathbb{LG}(n, 2n)$. This provides an understanding of the equivalence of these different-looking formulas, and it leads to new twistor-like formulas for 6D superamplitudes.

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arXiv2019

All Tree Amplitudes of 6D $(2,0)$ Supergravity: Interacting Tensor Multiplets and the $K3$ Moduli Space

We present a twistor-like formula for the complete tree-level S matrix of 6D $(2,0)$ supergravity coupled to $21$ abelian tensor multiplets. This is the low-energy effective theory that corresponds to Type IIB superstring theory compactified on a $\mathrm{K}3$ surface. The formula is expressed as an integral over the moduli space of certain rational maps of the punctured Riemann sphere. By studying soft limits of the formula, we are able to explore the local moduli space of this theory, ${SO(5,21)\over SO(5)\times SO(21)}$. Finally, by dimensional reduction, we also obtain a new formula for the tree-level S matrix of 4D $\mathcal{N}=4$ Einstein-Maxwell theory.

hep-th↗

arXiv2018

The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps

We present new formulas for $n$-particle tree-level scattering amplitudes of six-dimensional $\mathcal{N}=(1,1)$ super Yang-Mills (SYM) and $\mathcal{N}=(2,2)$ supergravity (SUGRA). They are written as integrals over the moduli space of certain rational maps localized on the $(n-3)!$ solutions of the scattering equations. Due to the properties of spinor-helicity variables in six dimensions, the even-$n$ and odd-$n$ formulas are quite different and have to be treated separately. We first propose a manifestly supersymmetric expression for the even-$n$ amplitudes of $\mathcal{N}=(1,1)$ SYM theory and perform various consistency checks. By considering soft-gluon limits of the even-$n$ amplitudes, we deduce the form of the rational maps and the integrand for $n$ odd. The odd-$n$ formulas obtained in this way have a new redundancy that is intertwined with the usual $\text{SL}(2, \mathbb{C})$ invariance on the Riemann sphere. We also propose an alternative form of the formulas, analogous to the Witten-RSV formulation, and explore its relationship with the symplectic (or Lagrangian) Grassmannian. Since the amplitudes are formulated in a way that manifests double-copy properties, formulas for the six-dimensional $\mathcal{N}=(2,2)$ SUGRA amplitudes follow. These six-dimensional results allow us to deduce new formulas for five-dimensional SYM and SUGRA amplitudes, as well as massive amplitudes of four-dimensional $\mathcal{N}=4$ SYM on the Coulomb branch.

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arXiv2017

M5-Brane and D-Brane Scattering Amplitudes

We present tree-level $n$-particle on-shell scattering amplitudes of various brane theories with $16$ conserved supercharges. These include the world-volume theory of a probe D3-brane or D5-brane in 10D Minkowski spacetime as well as a probe M5-brane in 11D Minkowski spacetime, which describes self interactions of an abelian tensor supermultiplet with 6D $(2,0)$ supersymmetry. Twistor-string-like formulas are proposed for tree-level scattering amplitudes of all multiplicities for each of these theories. The R symmetry of the D3-brane theory is shown to be $SU(4) \times U(1)$, and the $U(1)$ factor implies that its amplitudes are helicity conserving. Each of 6D theories (D5-brane and M5-brane) reduces to the D3-brane theory by dimensional reduction. As special cases of the general M5-brane amplitudes, we present compact formulas for examples involving only the self-dual $B$ field with $n=4,6,8$.

hep-th↗

arXiv2016

New Formulation of the Type IIB Superstring Action in $AdS_5 \times S^5$

Previous studies of the type IIB superstring in an ${AdS_5 \times S^5}$ background are based on a description of the superspace geometry as the quotient space $PSU(2,2|4)/SO(4,1) \times SO(5)$. This paper develops an alternative approach in which the Grassmann coordinates provide a nonlinear realization of $PSU(2,2|4)$ based on the quotient space $PSU(2,2|4)/SU(2,2) \times SU(4)$, and the bosonic coordinates are described as a submanifold of $SU(2,2) \times SU(4)$. This formulation keeps all bosonic symmetries manifest, and it provides the complete dependence on the Grassmann coordinates in terms of simple analytic expressions. It is used to construct the superstring world-sheet action in a form in which the $PSU(2,2|4)$ symmetry is manifest and kappa symmetry can be established. This formulation might have some advantages compared to previous ones, but this remains to be demonstrated.

hep-th↗

arXiv2014

Gauge Theories on the Coulomb branch

We construct the world-volume action of a probe D3-brane in $AdS_5 \times S^5$ with $N$ units of flux. It has the field content, symmetries, and dualities of the $U(1)$ factor of ${\cal N} =4$ $U(N+1)$ super Yang--Mills theory, spontaneously broken to $U(N) \times U(1)$ by being on the Coulomb branch, with the massive fields integrated out. This motivates the conjecture that it is the exact effective action, called a `highly effective action' (HEA). We construct an $SL(2,Z)$ multiplet of BPS soliton solutions of the D3-brane theory (the conjectured HEA) and show that it reproduces the electrically charged massive states that have been integrated out as well as magnetic monopoles and dyons. Their charges are uniformly spread on a spherical surface, called a `soliton bubble', which is interpreted as a phase boundary.

hep-th↗

arXiv2014

BPS Soliton Solutions of a D3-brane Action

The world-volume action of a probe D3-brane in $AdS_5 \times S^5$ with $N$ units of flux has the field content, symmetries, and dualities of the $U(1)$ factor of ${\cal N} = 4$ $U(N+1)$ super Yang--Mills theory, spontaneously broken to $U(N) \times U(1)$ by being on the Coulomb branch, with the massive fields integrated out. Thus, it might be the exact effective action (a highly effective action), or else a useful approximation to it. We construct an $SL(2,Z)$ multiplet of BPS soliton solutions of the D3-brane action and show that in the $N=1$ case they correspond to the electrically charged states that have been integrated out as well as magnetic monopoles and dyons. Their charges are uniformly spread on a spherical surface, a soliton bubble, which can be interpreted as a phase boundary. This picture is consistent with previous results in the string theory and field theory literature.

hep-th↗

arXiv2014

Yangian-Like Symmetry of Probe-Brane Actions

We demonstrate that world-volume actions describing probe branes in anti de Sitter space have an infinite-dimensional symmetry algebra that is reminiscent of Yangian symmetry. Two essential ingredients are responsible for this symmetry. The first is an inversion symmetry of anti de Sitter space. The second is the compensating gauge transformations that are required to properly describe global symmetries after gauge fixing the general coordinate invariance.

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arXiv2013

Highly Effective Actions

It is conjectured that the world-volume action of a probe D3-brane in an $AdS_5 \times S^5$ background of type IIB superstring theory, with one unit of flux, can be reinterpreted as the exact effective action (or highly effective action) for U(2), ${\cal N} = 4$ super Yang-Mills theory on the Coulomb branch. An analogous conjecture for $U(2)_k \times U(2)_{-k} $ ABJM theory is also presented. The main evidence supporting these conjectures is that the brane actions have all of the expected symmetries and dualities. Highly effective actions have general coordinate invariance, even though they describe nongravitational theories.

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arXiv2013

Multicharge Superstrings

There are an infinite number of type IIB superstrings in ten dimensions, called (p,q) strings, that are labeled by two distinct string charges. They can form string junctions and string networks. These are the key to understanding the Coulomb branch BPS spectrum of N=4 super Yang--Mills theories in four dimensions. Nongravitational theories that are analogous to type IIB superstring theory in some respects are the ADE (2,0) six-dimensional theories on the Coulomb branch. Each of them contains a finite number of half-BPS superstrings, which can be labeled by the root vectors of the Lie algebra. When the rank is greater than one, these strings can also form string junctions and string networks. The relationship between N=4 super Yang--Mills theories in four dimensions and the (2,0) theories in six dimensions can be explored by utilizing the duality between type IIB superstring theory compactified on a circle and M-theory compactified on a torus.

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arXiv2013

Higgs Bosons at 98 and 125 GeV at LEP and the LHC

We discuss NMSSM scenarios in which the lightest Higgs boson $h_1$ is consistent with the small LEP excess at about 98 GeV in $e^+e^- \to Zh$ with $h\to b\anti b$ and the heavier Higgs boson $h_2$ has the primary features of the LHC Higgs-like signals at 125 GeV, including an enhanced $γγ$ rate. Verification or falsification of the 98 GeV $h_1$ may be possible at the LHC during the 14 TeV run. The detection of the other NMSSM Higgs bosons at the LHC and future colliders is also discussed, as well as dark matter properties of the scenario under consideration.

hep-ph↗

arXiv2012

The Early History of String Theory and Supersymmetry

This lecture presents a brief overview of the early history of string theory and supersymmetry. It describes how the S-matrix theory program for understanding the strong nuclear force evolved into superstring theory, which is a promising framework for constructing a unified quantum theory of all forces including gravity. The period covered begins with S-matrix theory in the mid 1960s and ends with the widespread acceptance of superstring theory in the mid 1980s. Further details and additional references can be found in Schwarz (2007).

physics.hist-ph↗

arXiv2010

Some Recent Progress in AdS/CFT

Much of modern string theory research concerns AdS/CFT duality, or more generally, gauge/gravity duality. The main subjects are a) Testing and understanding such dualities by exploring how they work for systems with a lot of supersymmetry b) Constructing and exploring approximate string theory duals of QCD c) Applying gauge/gravity duality to other areas of physics such as condensed matter and nuclear physics. I will briefly discuss the first topic.

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