Heterotic String

Abstract

A new type of superstring theory is constructed as a chiral combination of the closed D = 26 bosonic and D = 10 fermionic strings. The theory is supersymmetric, Lorentz invariant, and free of tachyons. Consistency requires the gauge group to be Spin(32)/Z 2 or £ 8 x E%.PACS numbers: ll.30. Pb, 11.30.Ly, 12.10.En Recent interest in superstring unified field theories has been sparked by the discovery of Green and Schwarz 1 that nonorientable (type I) open and closed superstrings 2 with iV= 1 supersymmetry are finite and free of anomalies if the gauge group is SO(32). Previously the only consistent, anomaly-free 3 superstring theory was that of orientable (type II) N = 2 supersymmetric closed strings. The new theory has the advantage of already containing a large (and unique) gauge group. It is much easier to contemplate this theory producing the low-energy gauge group, as well as families of chiral massless fermions, upon compactification of the original ten dimensions. Witten has discussed some of the phenomenology of this theory and has shown that it is easy to imagine compactifications that yield an SU(5) theory with any number of standard fermionic generations. 4 The anomaly cancellation mechanism of Green and Schwarz is based on group theoretical properties of SO(32) which are shared by only one other semisimple Lie group, namely E%x E s . Such a group, however, cannot appear in the standard form of open-string theory, in which gauge groups are introduced by attaching quantum numbers to the ends of the string and Chan-Paton factors 5 to the scattering amplitudes. This procedure yields only the gauge groups SO(A0 and Sp(2A0. 6 The correspondence between the lowenergy limit of existing supersymmetric string theories with anomaly-free, Z) = 10, supergravity field theories suggests the existence of a new kind of string theory whose low-energy limit would have an E s x E% gauge group. Eschewing the Chan-Paton route to gauge groups for open strings, one might try to obtain fgXfg by compactifying a higher-dimensional closedstring theory. An important clue to how such a theory might arise is provided by the work of Frenkel and Kac. 7 J In this Letter we shall outline the construction of a new kind of closed-string theory, whose low-energy limit is Z> = 10, N=l supergravity coupled to supersymmetric Yang-Mills theory with gauge group Spin(32)/Z 2 or E s x E%. This theory is constructed as a hybrid of the Z> = 10 fermionic string and the Z> = 26 bosonic string, which preserves the appealing features of both. We show that the orientable, closed heterotic 8 string has an N = 1 supersymmetric spectrum of states of positive metric, is free of tachyons and is Lorentz invariant. The requirement that gravitational and gauge anomalies be absent necessitates the compactification of the extra sixteen bosonic coordinates of the heterotic string on a maximal torus of determined radius, in a way that produces gauge groups Spin(32)/Z 2 or E s xE s .We further argue that the heterotic loop diagrams are free of all infinities-thus...

Stringy symmetries and their high-energy limits

“…In fact, once we settle on the quantum theory of a free string, the forms of the interactions and thus symmetries of all string states are fixed by the quantum consistency of the theory. For example, the massless gauge symmetries of 10D Heterotic string [1] were determined to be SO(32) or E 2 8 by the string one-loop consistency or modular invariance of the theory. Some stringy Einstein-Yang-Mills type symmetries with symmetry parameters containing both Einstein and Yang-Mills index were proposed in Ref [2].…”

From the Heterotic String Quartet to the Cosmic Dark Matter, Dark Energy and Ordinary Energy Symphony

“…To avoid the mind boggling questions surrounding the true meaning of dimensionality in general [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and how it is used in the present work in particular, we stress the following: We are assuming that we are at the very beginning of say "creation" and at such a high energy scale corresponding to extremely small distances where in this spacetime "primordial soup" so to speak, the distinction between symmetry, dimensions and quantum particles almost vanishes [15][16][17]. Thus whenever we say particles here, we mean pre-quantum particle-like states which will result from symmetry breaking of a corresponding Lie group of certain dimensionality [15][16][17][18][19]. Something similar will be assumed with regard to the word wave with which we mean prequantum wave of the pre-quantum particle [19][20][21][22][23][24][25][26][27][28].…”

“…Having clarified our "somewhat fuzzy" terminology we turn our attention to the main theory upon which the present model and analysis is based, namely the heterotic string theory [14,17,18]. The essence of this theory is lucidly explained in many papers and text books notably by the creators of the theory, namely a group around Nobel Laureate David Gross [17,18] which is often fondly referred to as the "Princeton quartet" [17,18].…”

“…The essence of this theory is lucidly explained in many papers and text books notably by the creators of the theory, namely a group around Nobel Laureate David Gross [17,18] which is often fondly referred to as the "Princeton quartet" [17,18]. Never the less because we will present this theory in the next section with a minor twist here and there, we felt it pertinent to give here a brief account of the quintessential idea behind heterotic string theory seen from our "pure dark energy and dark matter" explanation view point [20][21][22][23][24][25][26][27].…”

Self-duality beyond chiral p-form actions

“…In D = 2 dimensional space-time, chiral bosons (p = 0) occur as basic ingredients and elements in the formulation of heterotic strings [1] and in a number of statistical systems [2]. In D > 2 dimensional space-time, chiral 2-and 4-forms are relevant to the M-theory five-brane [3,4] and type IIB supergravity [5][6][7], respectively.…”