scholarly journals Rank $Q$ E-string on a torus with flux

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Sara Pasquetti ◽  
Shlomo Razamat ◽  
Matteo Sacchi ◽  
Gabi Zafrir
Keyword(s):  
Simple Model ◽  
String Theory ◽  
Domain Wall ◽  
Dimensional Reduction ◽  
Partition Functions ◽  
Global Symmetry ◽  
Coulomb Branch ◽  
Abelian Subgroups ◽  
Chiral Superfields

We discuss compactifications of rank QQ E-string theory on a torus with fluxes for abelian subgroups of the E_8E8 global symmetry of the 6d6d SCFT. We argue that the theories corresponding to such tori are built from a simple model we denote as E[USp(2Q)]E[USp(2Q)]. This model has a variety of non trivial properties. In particular the global symmetry is USp(2Q)\times USp(2Q)\times U(1)^2USp(2Q)×USp(2Q)×U(1)2 with one of the two USp(2Q)USp(2Q) symmetries emerging in the IR as an enhancement of an SU(2)^QSU(2)Q symmetry of the UV Lagrangian. The E[USp(2Q)]E[USp(2Q)] model after dimensional reduction to 3d3d and a subsequent Coulomb branch flow is closely related to the familiar 3d3dT[SU(Q)]T[SU(Q)] theory, the model residing on an S-duality domain wall of 4d4d\mathcal{N}=4𝒩=4SU(Q)SU(Q) SYM. Gluing the E[USp(2Q)]E[USp(2Q)] models by gauging the USp(2Q)USp(2Q) symmetries with proper admixtures of chiral superfields gives rise to systematic constructions of many examples of 4d4d theories with emergent IR symmetries. We support our claims by various checks involving computations of anomalies and supersymmetric partition functions. Many of the needed identities satisfied by the supersymmetric indices follow directly from recent mathematical results obtained by E. Rains.

scholarly journals Domain walls in 4d $$ \mathcal{N} $$ = 1 SYM

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Diego Delmastro ◽  
Jaume Gomis
Keyword(s):  
Domain Wall ◽  
Domain Walls ◽  
Simons Theory ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Yang Mills ◽  
Stable Domain ◽  
Coxeter Number ◽  
Topological Quantum ◽  
Simply Connected

Abstract 4d$$ \mathcal{N} $$ N = 1 super Yang-Mills (SYM) with simply connected gauge group G has h gapped vacua arising from the spontaneously broken discrete R-symmetry, where h is the dual Coxeter number of G. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We put forward an explicit answer to this question for all the domain walls for G = SU(N), Sp(N), Spin(N) and G2, and for the minimal domain wall connecting neighboring vacua for arbitrary G. We propose that the domain wall theories support specific nontrivial topological quantum field theories (TQFTs), which include the Chern-Simons theory proposed long ago by Acharya-Vafa for SU(N). We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions twisted by global symmetries of SYM computed in the ultraviolet with those computed in our proposed infrared TQFTs. A crucial element in this matching is constructing the Hilbert space of spin TQFTs, that is, theories that depend on the spin structure of spacetime and admit fermionic states — a subject we delve into in some detail.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

scholarly journals LOOP VARIABLES AND GAUGE-INVARIANT INTERACTIONS — II

2001 ◽  
Vol 16 (10) ◽  
pp. 1679-1701 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Gauge Transformation ◽  
Dimensional Reduction ◽  
Mass Shell ◽  
Bosonic String ◽  
Higher Dimension ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Variable Approach

We continue the discussion of our previous paper on writing down gauge-invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space–time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba–Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the free mass shell).

scholarly journals FROM p-BRANES TO COSMOLOGY

1999 ◽  
Vol 14 (26) ◽  
pp. 4121-4142 ◽  
Author(s):  
H. LÜ ◽  
S. MUKHERJI ◽  
C. N. POPE
Keyword(s):  
String Theory ◽  
Effective Action ◽  
Dimensional Reduction ◽  
Cosmological Models ◽  
Cosmological Solutions ◽  
M Theory ◽  
The Relationship

We study the relationship between static p-brane solitons and cosmological solutions of string theory or M theory. We discuss two different ways in which extremal p-branes can be generalized to nonextremal ones, and show how wide classes of recently discussed cosmological models can be mapped into nonextremal p-brane solutions of one of these two kinds. We also extend previous discussions of cosmological solutions to include some that make use of cosmological-type terms in the effective action that can arise from the generalized dimensional reduction of string theory or M theory.

scholarly journals Inner products in integrable Richardson-Gaudin models

2017 ◽  
Vol 3 (4) ◽  
Author(s):  
Pieter W. Claeys ◽  
Dimitri Van Neck ◽  
Stijn De Baerdemacker
Keyword(s):  
Domain Wall ◽  
Integrable Models ◽  
Partition Functions ◽  
Dual Representation ◽  
Determinant Formula ◽  
Quadratic Equations ◽  
Conserved Charges ◽  
Inner Products ◽  
Gaudin Models ◽  
Bethe Equations

We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula.Furthermore, this framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.

scholarly journals A simple model for calculating magnetic nanowire domain wall fringing fields

2012 ◽  
Vol 45 (9) ◽  
pp. 095002 ◽  
Author(s):  
Adam D West ◽  
Thomas J Hayward ◽  
Kevin J Weatherill ◽  
Thomas Schrefl ◽  
Dan A Allwood ◽  
...  
Keyword(s):  
Simple Model ◽  
Domain Wall ◽  
Magnetic Nanowire ◽  
Fringing Fields

scholarly journals What prevents gravitational collapse in string theory?

2016 ◽  
Vol 25 (12) ◽  
pp. 1644018 ◽  
Author(s):  
Samir D. Mathur
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
String Theory ◽  
Quantum Gravity ◽  
State Space ◽  
Dimensional Reduction ◽  
Extra Dimension ◽  
Mass Formula ◽  
Compact Dimension ◽  
Classical Gravity

It is conventionally believed that if a ball of matter of mass [Formula: see text] has a radius close to [Formula: see text][Formula: see text]GM then it must collapse to a black hole. But string theory microstates (fuzzballs) have no horizon or singularity, and they do not collapse. We consider two simple examples from classical gravity to illustrate how this violation of our intuition happens. In each case, the ‘matter’ arises from an extra compact dimension, but the topology of this extra dimension is not trivial. The pressure and density of this matter diverge at various points, but this is only an artifact of dimensional reduction; thus, we bypass results like Buchadahl’s theorem. Such microstates give the entropy of black holes, so these topologically nontrivial constructions dominate the state space of quantum gravity.

scholarly journals Domain Walls from M-Branes

1997 ◽  
Vol 12 (15) ◽  
pp. 1087-1094 ◽  
Author(s):  
H. Lü ◽  
C. N. Pope
Keyword(s):  
Domain Wall ◽  
Dimensional Reduction ◽  
Domain Walls ◽  
Additional Term ◽  
Cosmological Term ◽  
Domain Wall Solution ◽  
Toroidal Compactifications ◽  
Four Manifolds ◽  
M Theory ◽  
Kaluza Klein

We discuss the vertical dimensional reduction of M-sbranes to domain walls in D=7 and D=4, by dimensional reduction on Ricci-flat four-manifolds and seven-manifolds. In order to interpret the vertically-reduced five-brane as a domain wall solution of a dimensionally-reduced theory in D=7, it is necessary to generalize the usual Kaluza–Klein ansatz, so that the three-form potential in D=11 has an additional term that can generate the necessary cosmological term in D=7. We show how this can be done for general four-manifolds, extending previous results for toroidal compactifications. By contrast, no generalization of the Kaluza–Klein ansatz is necessary for the compactification of M-theory to a D=4 theory that admits the domain-wall solution coming from the membrane in D=11.

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