List of errata for publications
1.
Corrections: The r.h.s. of eq. (33) equals P/3. The decomposition of n(a) in lemma (3.2) is only general for N=2 and the conclussion that P is always even without twist only holds for that case (I thank Andreas Wipf for pointing this out). In lemma (4.1) factors 1/2 were forgotten in the definitions of mi and ai. First line of lemma (A.2) replace the first j for the set labels by i. Also it is more conventional to take -P as the Pontryagin index.

2.
Corrections: In eq. (A.2) z(N-1)/2 should be for both cases z-(N-1)/2, whereas on the diagonal zM-1 should be zN-1

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.
Corrections: In eq. (3) the argument of the sin needs to halved. The integration in eq. (4) needs to run between the g dependent turning points

15.
Corrections: In eq. (4.13) the Airy function should be replaced by its derivative, see also eq. (94) in 38. which also corrects in the exponent of eq. (5.45) the power of the subleading term

16.
Corrections: Below eq. (47) one should read MS for MS-bar. At the end of App. A the sum over a2n+1 runs from n=0

17.
Corrections: In eq. (3.41) one derivative too many. Some signs in eqs. (4.22) and (4.26) are wrong. In eq. (5.20) the factor -1/2 should be dropped In eq. (8.18) replace the first factor, 4(1+i+4j), by 4i(1+i+4j). Table I, lower part, lists norms of X, rather than P. Eq. (8.34) applies for q=q' only. In eq. (8.35) put m=q,m'=q' and multiply with hatN(n,q)hatN(n',q')/2. Multiply the right hand side of eq. (8.42) with r4.

18.
Corrections: Sign error in eq. (22), see 35., sect. 2. Below eq. (35) reference should have been made to eq. (6) instead of (5)

19.
Corrections: 2N1/2 should be replaced by (2N)1/2 in eqs. (4a-c)

20.

21.

22.
Correction: typos in eqs. (2.3-4), (2.6), (2.8), (2.9), (2.23), (3.12), (A.9), (B.7) and in table 1 (alpha3 and kappa8 sign change), table 7 (energy of E+ at g=1.4 corrected). See also 27. (sect. 6) and 30. (sect. I.2) for the issue of assigning correct quantum numbers to the T2 and T1 glueball states (I thank Claus Vohwinkel for pointing this out)

23.

24.
Printer's error (see erratum): Wrong figure printed. Additional correction: missing brackets in eq. (16)

25.

26.

27.

28.
Corrections: typos in eqs. (1), (16), (25), (30), (32) and (36)

29.

30.
Corrections, typo in eq. (3.7) and revision of tab. 1

31.
Corrections: typo in eq. (3) and alpha2 in tab. 1

32.

33.

34.

35.
Corrections: just above eqs. (2.8) a c2 missing, typos in eqs. (3.6), (3.10), (4.23), (4.27), (4.33), (4.36), (4.40), (4.42), (4.46), (5.1), 1st line above eqs. (2.8) and (4.46), 1st line in tab. 3

36.
Correction: In Eqs.(2.1) and (2.3) replace 2 Sqrt Trad(X) by Trad Sqrt(X).

37.
Corrections: typos in eqs. (8), (16) and (17); See also 40. for a correction concerning sect. 3 and 51. for a note on the non-contractible sphere argument

38.

39.
Corrections: typos in eqs. (69-72) and (77-79). See also 43. at the end of sect. 3

40.

41.

42.

43.

44.

45.

46.

47.
Corrections: In eq. (8) and the expression below eq. (7) some terms were not listed, see 52., eq. (21) and below

48.
Corrections: two minor typos

49.

50.

51.

52.

53.
Corrections: typos in eqs. (31) and (41), as well as factors a half and signs

54.

55.

56.

57.

58.

59.

60.

61.

62.
Note added in proof in Journal version. Printer's error: in eq.(5) the closing bracket in the third line from the bottom, should be at the end of the line below that (i.e. both terms need to be multiplied with pi rho2). Additional corrections: minus sign just above and in eq.(7); in the figure the action density was cut off below 1/(2e), instead of 1/e. In eq.(20), top line, the argument of the exponent has to change sign.

63.
For eq.(7), the boundary term has the opposite sign. Eq.(38), the exponent in the Fourier series of lambda has to change sign. Furthermore, lambda-hat-dagger(z')lambda-hat(z) has z and z' interchanged. Eq.(76) has an overall minus sign. The result in eq. (97) is four times too large, the overall factor two should have been a half. In eq.(100) r and s should be interchanged. Printer's error: In eq.(A.3) the first line, (z-z) should be replaced by (z-z').

64.
Corrections: Figure 1 was cut off below 1/(2e), instead of 1/e. In eq.(9) the index 3 on eta-bar and a constant term for A0 was omitted.

65.

66.
Corrections in the caption of Figure 1: the first and third mass parameter were interchanged, they should read (nu1,nu2,nu3)=(0.25,0.35,0.4). The second component of the position of the first consitituent had the wrong sign and should read y1=(-1/2,-1/2,0). Finally the action was cut off below 1/(2e), instead of 1/e.

67.
Corrections: Three lines below eq.(3) the mass has to be divided by 2. Figures 1 and 3 were cut off below 1/(2e), instead of 1/e. Figure 2 was cut off below 1/(2e2), instead of 1/e2. In the caption of figure 1 the coordinates of the first constituent should read y1=(-1/2,-1/2,0).

68.
Corrections: The reference to Eq.(40) in Ref.[8b] just above eq.(16) should be replaced by a reference to Eq.(40) in Ref.[7b], the second paper (63.) listed in Ref.[7].

69.

70.

71.

72.
The subscript z that appears in Eq.(6) for the Greens function should be x (as in Eqs.(5) and (8)).

73.

74.
In Eq.(4) the right hand side should be multiplied with 1/2.

75.
In Eq.(6) the index on f should be x instead of z. Just above Eq.(9), it should have been stated that the result quoted for SU(2) is for either z=0 (m=1), using that mu2= -mu1=nu1/2, or z=1/2 (m=2), using that 1/2-mu2=mu3-1/2=1+mu1-1/2=nu2/2 . Eq.(9) generalizes this to arbitrary z and SU(N). For Eq.(21) and the SU(N) result below it, the cores of the constituents are assumed not to overlap, in which case the result is valid up to exponentially small corrections.

76.
For Eqs.(13,14) the cores of the constituents are assumed not to overlap, in which case the result is valid up to exponentially small corrections.

77.

78.
Corrections (in the hep-ph version): One factor of Pi too many for the r.h.s. of Eq. (8). In Eq.(17) and (19), and at the top of pg. 23, replace 2 Sqrt Trad(X) by Trad Sqrt(X). Third line of sect. 3.5, "is crucial to preserve the gauge symmetry" should read "is crucial to preserve the supersymmetry". Additional correction: 9th line above section 6, "Beyond g(R) ~ 2.8" should read "Beyond g(R) ~ 2.35" (or "Beyond f ~ 0.28").

79.

80.

81.
In Eq.(5) the minus sign has to be replaced by a plus.

82.

83.
New results on the groundstate wave function have been added (3 Jan. 2002). In addition correction of minor typo's, an imporved discussion around Eq.(2), and below Eq.(10), as well as adding on pg. 8 (6th line of 2nd paragraph) a reference to Smilga's effective Hamiltonian analysis in the supersymmetric QED case. All corrections and additions have now been implemented for v.2 on the archive.
Additional correction: In Eq.(23), 1st line, replace xja by xj.

84.
In Eq.(13) cos(2pi t) should be cos(2pi t/beta) and in Eq.(15) e-2pi i t should be e-2pi i t/beta.
One could also divide the righthand side of Eq.(14), and hence also the Greens function, by beta. In that case many factors of 1/beta would then get absorbed in the Greens function. This would have been the more natural choice from the point of view of fourier transforming the ADHM data.

85.
In the figure which illustrates Eq.(71), the index + and - for the expression of Sigmam should be interchanged. It should read, as in Eq.(71), R+m-1(mum)+ Sm+R-m(mum). (Has been corrected in the published version).
Additional corrections: In Eq.(5), take the anti-hermitian part. Just below Eq.(13), A-hat is of course anti-hermitian. In Eq.(69), Rm should have been shown without argument as in the definition. In the 2nd line below Eq.(73), Trk should be replaced by Tr2k. In Eq.(80), F should be replaced by script F (and the index on mu should be m instead of n). Eq.(88) uses e. (R2-R1)=S2, which should be -S2 (since S2=Y2- Y1 and Rm=x-Ym, with Ym=eYm). Hence everywhere in Eqs.(88-90) change e to -e (or interchange R2, r2(i) with R1, r1(i)). The final result remains unaffected.

86.

87.
Third line below Eq.(23), mu should have an index m in the expression for fm. In Eq.(39) an overall factor Abs(zeta) should be inserted and in the line below this equation the weight factor has to be conjugated. In Eq.(78) a term 2(k x3|x|)2 was lost in the typesetting. All these corrections have been implemented in the published version.
Additional corrections: For the 2nd line below Eq.(3) zmu should strictly speaking be replaced by z deltamu0. In writing Eq.(28) we should have specified that z' has to be bigger or equal to z and valid up to and including the boundaries of the interval on which it is defined. (When z' is smaller than z, simply interchange z and z' -- in this limit the function is real). Eq.(61) should read D2=4 (c3-c2) instead of D2=(c3 -c2)/4. Just above Eq.(67) it should have read that alpha2=-alpha1=alpha/(4 Pi), instead of alpha/Pi. In Eq.(68) the indentity matrix is of course 2X2 (and not 1X1). From Eq.(71) until (but not including) Eq.(72) there were three instances where a factor pi in front of rho2 was missing.
In Appendix A we should have defined more explictely that Fm (so without the z-dependence specified) stands for Fm(mum+1).

88.

89.
In Eq.(28) a factor a half is missing in front of the commutator term.

90.

91.
Corrections implemented in the published version, and in v2 on the archive: In Eq.(38) a factor i was forgotten for the term with the Jacobi elliptic functions. In the captions of figures 1, 3 and 4, the scales of the zero-mode densities are enhanced by an additional factor 2pi2. Some factors of 2pi were also forgotten in quoting the time dependent values of the action density in the second paragraph above section 5.
Additional corrections: In the second identity of Eq.(29) a sign on the rhs should be inserted. In footnote (4) we used (d/dz)det(Y)=Tr(Y-1 dY/dz) det(Y), but forgot to write the det(Y) factor. It does not affect the result since the Nahm equation implies Tr(Y-1dY/dz)=0. Using the already established fact that det(Y) is conserved would have been easier at this point.

92.

93.

94.

95.

96.

97.

98.

99.

100.